commit 7862d4e51530dc1d97fb20b63060d017f04b6a24
parent 92fe0e599cf079aea24fa75af8890fbc05bb078d
Author: Sebastiano Tronto <sebastiano.tronto@gmail.com>
Date: Sun, 6 Sep 2020 19:29:27 +0200
Added exercises and some pages to the slides
Diffstat:
16 files changed, 267 insertions(+), 137 deletions(-)
diff --git a/README.md b/README.md
@@ -4,7 +4,7 @@ Here you can find the slides and the exercises for the course
"Elementary Logic" (University of Luxembourg, PrepCamp 2020).
For the slides, go in the ``slides`` folder and look for the file
-``preplogic-slides.pdf''.
+``preplogic-slides.pdf``.
-For the exercises, go in the ``exercises'' folder and look for the file
-``preplogic-exercises.pdf''.
+For the exercises, go in the ``exercises`` folder and look for the file
+``preplogic-exercises.pdf``.
diff --git a/exercises/preplogic-exercises.fdb_latexmk b/exercises/preplogic-exercises.fdb_latexmk
@@ -1,5 +1,5 @@
# Fdb version 3
-["pdflatex"] 1599407243 "preplogic-exercises.tex" "preplogic-exercises.pdf" "preplogic-exercises" 1599407243
+["pdflatex"] 1599413298 "preplogic-exercises.tex" "preplogic-exercises.pdf" "preplogic-exercises" 1599413298
"/usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc" 1594687104 2900 1537cc8184ad1792082cd229ecc269f4 ""
"/usr/share/texmf-dist/fonts/map/fontname/texfonts.map" 1594687104 3524 cb3e574dea2d1052e39280babc910dc8 ""
"/usr/share/texmf-dist/fonts/map/pdftex/updmap/pdftex.map" 1594687104 4851843 f8aac22e46e9a458223e5c13b1e20998 ""
@@ -26,18 +26,24 @@
"/usr/share/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm" 1594687104 1116 933a60c408fc0a863a92debe84b2d294 ""
"/usr/share/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1594687104 1120 8b7d695260f3cff42e636090a8002094 ""
"/usr/share/texmf-dist/fonts/tfm/public/cm/cmti10.tfm" 1594687104 1480 aa8e34af0eb6a2941b776984cf1dfdc4 ""
+ "/usr/share/texmf-dist/fonts/tfm/public/cm/cmtt12.tfm" 1594687104 772 9a936b7f5e2ff0557fce0f62822f0bbf ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb" 1594687104 34811 78b52f49e893bcba91bd7581cdc144c0 ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1594687104 32080 340ef9bf63678554ee606688e7b5339d ""
+ "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb" 1594687104 30251 6afa5cb1d0204815a708a080681d4674 ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1594687104 36299 5f9df58c2139e7edcf37c8fca4bd384d ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi5.pfb" 1594687104 37912 77d683123f92148345f3fc36a38d9ab1 ""
+ "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb" 1594687104 36281 c355509802a035cadc5f15869451dcee ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1594687104 35752 024fb6c41858982481f6968b5fc26508 ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1594687104 32722 d7379af29a190c3f453aba36302ff5a9 ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb" 1594687104 32362 179c33bbf43f19adbb3825bb4e36e57a ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1594687104 32762 224316ccc9ad3ca0423a14971cfa7fc1 ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1594687104 32569 5e5ddc8df908dea60932f3c484a54c0d ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb" 1594687104 37944 359e864bd06cde3b1cf57bb20757fb06 ""
+ "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt12.pfb" 1594687104 24252 1e4e051947e12dfb50fee0b7f4e26e3a ""
"/usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb" 1594687104 34694 ad62b13721ee8eda1dcc8993c8bd7041 ""
"/usr/share/texmf-dist/fonts/type1/public/cm-super/sfrm1000.pfb" 1594687104 138258 6525c253f16cededa14c7fd0da7f67b2 ""
+ "/usr/share/texmf-dist/tex/generic/iftex/iftex.sty" 1594687104 6501 4011d89d9621e0b0901138815ba5ff29 ""
+ "/usr/share/texmf-dist/tex/generic/iftex/ifvtex.sty" 1594687104 1057 525c2192b5febbd8c1f662c9468335bb ""
"/usr/share/texmf-dist/tex/latex/amscls/amsthm.sty" 1594687104 12594 0d51ac3a545aaaa555021326ff22a6cc ""
"/usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1594687104 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c ""
"/usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1594687104 13829 94730e64147574077f8ecfea9bb69af4 ""
@@ -51,12 +57,14 @@
"/usr/share/texmf-dist/tex/latex/base/article.cls" 1594687104 20023 e427dd9e17e239bf926ef3aab67fe35e ""
"/usr/share/texmf-dist/tex/latex/base/inputenc.sty" 1594687104 5050 8933a39ad74377accd18991c5eb90c58 ""
"/usr/share/texmf-dist/tex/latex/base/size10.clo" 1594687104 8446 9874cccac5fee462272c582807dbbf56 ""
+ "/usr/share/texmf-dist/tex/latex/geometry/geometry.sty" 1594687104 41601 9cf6c5257b1bc7af01a58859749dd37a ""
+ "/usr/share/texmf-dist/tex/latex/graphics/keyval.sty" 1594687104 2590 e3b24ff953e5b58d924f163d25380312 ""
"/usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def" 1594687104 25742 5de23a2d2bc67a3139433e702e64a437 ""
"/usr/share/texmf-dist/web2c/texmf.cnf" 1597672114 39446 755423e82e7afb756f49b242a15f4ec2 ""
"/usr/share/texmf-var/web2c/pdftex/pdflatex.fmt" 1598712773 2434818 64d78922a5d2a9baf6bf1beec95a9374 ""
- "preplogic-exercises.aux" 1599407243 398 c1412237ecba2ce936c17ace596c30a6 "pdflatex"
- "preplogic-exercises.tex" 1599407242 3546 94e18075fe4f9c11a865c64ac581a692 ""
+ "preplogic-exercises.aux" 1599413298 398 c1412237ecba2ce936c17ace596c30a6 "pdflatex"
+ "preplogic-exercises.tex" 1599413295 4576 b03ca92fc16bbca83f264a2bb3016bef ""
(generated)
- "preplogic-exercises.log"
- "preplogic-exercises.pdf"
"preplogic-exercises.aux"
+ "preplogic-exercises.pdf"
+ "preplogic-exercises.log"
diff --git a/exercises/preplogic-exercises.fls b/exercises/preplogic-exercises.fls
@@ -25,6 +25,14 @@ INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty
+INPUT /usr/share/texmf-dist/tex/latex/geometry/geometry.sty
+INPUT /usr/share/texmf-dist/tex/latex/geometry/geometry.sty
+INPUT /usr/share/texmf-dist/tex/latex/graphics/keyval.sty
+INPUT /usr/share/texmf-dist/tex/latex/graphics/keyval.sty
+INPUT /usr/share/texmf-dist/tex/generic/iftex/ifvtex.sty
+INPUT /usr/share/texmf-dist/tex/generic/iftex/ifvtex.sty
+INPUT /usr/share/texmf-dist/tex/generic/iftex/iftex.sty
+INPUT /usr/share/texmf-dist/tex/generic/iftex/iftex.sty
INPUT /usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def
INPUT /usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def
INPUT preplogic-exercises.aux
@@ -54,6 +62,7 @@ INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd
INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
+INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmtt12.tfm
INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm
INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm
INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm
@@ -73,13 +82,16 @@ INPUT preplogic-exercises.aux
INPUT /usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb
+INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi5.pfb
+INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb
+INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt12.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb
INPUT /usr/share/texmf-dist/fonts/type1/public/cm-super/sfrm1000.pfb
diff --git a/exercises/preplogic-exercises.log b/exercises/preplogic-exercises.log
@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/VoidLinux) (preloaded format=pdflatex 2020.8.29) 6 SEP 2020 17:47
+This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/VoidLinux) (preloaded format=pdflatex 2020.8.29) 6 SEP 2020 19:28
entering extended mode
restricted \write18 enabled.
file:line:error style messages enabled.
@@ -100,52 +100,109 @@ Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
+)) (/usr/share/texmf-dist/tex/latex/geometry/geometry.sty
+Package: geometry 2020/01/02 v5.9 Page Geometry
+ (/usr/share/texmf-dist/tex/latex/graphics/keyval.sty
+Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
+\KV@toks@=\toks28
+) (/usr/share/texmf-dist/tex/generic/iftex/ifvtex.sty
+Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. Use iftex instead.
+ (/usr/share/texmf-dist/tex/generic/iftex/iftex.sty
+Package: iftex 2020/03/06 v1.0d TeX engine tests
))
-\c@exercise=\count187
+\Gm@cnth=\count187
+\Gm@cntv=\count188
+\c@Gm@tempcnt=\count189
+\Gm@bindingoffset=\dimen144
+\Gm@wd@mp=\dimen145
+\Gm@odd@mp=\dimen146
+\Gm@even@mp=\dimen147
+\Gm@layoutwidth=\dimen148
+\Gm@layoutheight=\dimen149
+\Gm@layouthoffset=\dimen150
+\Gm@layoutvoffset=\dimen151
+\Gm@dimlist=\toks29
+)
+\c@exercise=\count190
(/usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def
File: l3backend-pdfmode.def 2020-06-03 L3 backend support: PDF mode
-\l__kernel_color_stack_int=\count188
+\l__kernel_color_stack_int=\count191
\l__pdf_internal_box=\box47
) (./preplogic-exercises.aux)
\openout1 = `preplogic-exercises.aux'.
-LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12.
-LaTeX Font Info: ... okay on input line 12.
-LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12.
-LaTeX Font Info: ... okay on input line 12.
-LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12.
-LaTeX Font Info: ... okay on input line 12.
-LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12.
-LaTeX Font Info: ... okay on input line 12.
-LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 12.
-LaTeX Font Info: ... okay on input line 12.
-LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12.
-LaTeX Font Info: ... okay on input line 12.
-LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12.
-LaTeX Font Info: ... okay on input line 12.
-LaTeX Font Info: Trying to load font information for U+msa on input line 13.
- (/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd
+LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 13.
+LaTeX Font Info: ... okay on input line 13.
+LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 13.
+LaTeX Font Info: ... okay on input line 13.
+LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 13.
+LaTeX Font Info: ... okay on input line 13.
+LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 13.
+LaTeX Font Info: ... okay on input line 13.
+LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 13.
+LaTeX Font Info: ... okay on input line 13.
+LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 13.
+LaTeX Font Info: ... okay on input line 13.
+LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 13.
+LaTeX Font Info: ... okay on input line 13.
+
+*geometry* driver: auto-detecting
+*geometry* detected driver: pdftex
+*geometry* verbose mode - [ preamble ] result:
+* driver: pdftex
+* paper: a4paper
+* layout: <same size as paper>
+* layoutoffset:(h,v)=(0.0pt,0.0pt)
+* modes:
+* h-part:(L,W,R)=(89.62709pt, 418.25368pt, 89.6271pt)
+* v-part:(T,H,B)=(56.9055pt, 686.7347pt, 101.40665pt)
+* \paperwidth=597.50787pt
+* \paperheight=845.04684pt
+* \textwidth=418.25368pt
+* \textheight=686.7347pt
+* \oddsidemargin=17.3571pt
+* \evensidemargin=17.3571pt
+* \topmargin=-52.36449pt
+* \headheight=12.0pt
+* \headsep=25.0pt
+* \topskip=10.0pt
+* \footskip=30.0pt
+* \marginparwidth=57.0pt
+* \marginparsep=11.0pt
+* \columnsep=10.0pt
+* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
+* \hoffset=0.0pt
+* \voffset=0.0pt
+* \mag=1000
+* \@twocolumnfalse
+* \@twosidefalse
+* \@mparswitchfalse
+* \@reversemarginfalse
+* (1in=72.27pt=25.4mm, 1cm=28.453pt)
+
+LaTeX Font Info: Trying to load font information for U+msa on input line 14.
+(/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
)
-LaTeX Font Info: Trying to load font information for U+msb on input line 13.
+LaTeX Font Info: Trying to load font information for U+msb on input line 14.
(/usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
) [1
{/usr/share/texmf-dist/fonts/map/pdftex/updmap/pdftex.map}] [2] (./preplogic-exercises.aux) )
Here is how much of TeX's memory you used:
- 1629 strings out of 480478
- 20291 string characters out of 5905927
- 258779 words of memory out of 5000000
- 17679 multiletter control sequences out of 15000+600000
- 540575 words of font info for 56 fonts, out of 8000000 for 9000
+ 2168 strings out of 480478
+ 27947 string characters out of 5905927
+ 275547 words of memory out of 5000000
+ 18202 multiletter control sequences out of 15000+600000
+ 540744 words of font info for 57 fonts, out of 8000000 for 9000
1141 hyphenation exceptions out of 8191
- 30i,13n,31p,234b,251s stack positions out of 5000i,500n,10000p,200000b,80000s
-{/usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc}</usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi5.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb></usr/share/texmf-dist/fonts/type1/public/cm-super/sfrm1000.pfb>
-Output written on preplogic-exercises.pdf (2 pages, 125146 bytes).
+ 30i,16n,31p,234b,270s stack positions out of 5000i,500n,10000p,200000b,80000s
+{/usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc}</usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi5.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb></usr/share/texmf-dist/fonts/type1/public/cm-super/sfrm1000.pfb>
+Output written on preplogic-exercises.pdf (2 pages, 146771 bytes).
PDF statistics:
- 60 PDF objects out of 1000 (max. 8388607)
- 43 compressed objects within 1 object stream
+ 72 PDF objects out of 1000 (max. 8388607)
+ 52 compressed objects within 1 object stream
0 named destinations out of 1000 (max. 500000)
1 words of extra memory for PDF output out of 10000 (max. 10000000)
diff --git a/exercises/preplogic-exercises.pdf b/exercises/preplogic-exercises.pdf
Binary files differ.
diff --git a/exercises/preplogic-exercises.synctex.gz b/exercises/preplogic-exercises.synctex.gz
Binary files differ.
diff --git a/exercises/preplogic-exercises.tex b/exercises/preplogic-exercises.tex
@@ -3,11 +3,12 @@
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
+\usepackage[top=2cm]{geometry}
\theoremstyle{definition} \newtheorem{exercise}{Exercise}[section]
-\author{Sebastiano Tronto (uni.lu)}
-\title{Elementary logic exercises (Prep Camp 2020)}
+\author{Sebastiano Tronto (\texttt{sebastiano.tronto@uni.lu})}
+\title{Elementary Logic exercises (Prep Camp 2020)}
\begin{document}
\maketitle
@@ -15,7 +16,7 @@
\section{Logical operations}
\begin{exercise}
- Determine if the following statement are \textbf{true} or \textbf{false}:
+ Determine if the following statements are \textbf{true} or \textbf{false}:
\begin{enumerate}
\item ``Today is Tuesday or Germany has more inhabitants than Luxembourg''
\item ``$7$ is odd and $2+2=5$''
@@ -84,21 +85,35 @@ here}'' ?
\section{Quantifiers}
\begin{exercise}
+ Write the negation of the following statements:
+ \begin{enumerate}
+ \item $\exists x\in \mathbb N,\, x^2-2=0$
+ \item ``Every prime number is odd''
+ \item ``Every person I have met likes pizza''
+ \item ``There is at least one number greater than $7$''
+ \item $\forall x\in \mathbb N,\,x\geq 0$
+ \item $\forall x\in \mathbb Z,\,(\exists y\in\mathbb Z,\,x+y=0)$
+ \end{enumerate}
+\end{exercise}
+
+\begin{exercise}
There is another quantifier that we did not cover in the lecture, namely
$\exists!$ (read ``there exists exactly one''). For example, the sentence
``\emph{there exists exactly one natural number x such that x+2=5}'' can be
- written in symbols as ``$\exists!x\in \mathbb N,\,x+2=5$.
+ written in symbols as ``$\exists!x\in \mathbb N,\,x+2=5$''.
+
In this exercise, your task is to give a formal definition of this quantifier
using the logical symbols that we have defined in class. In particular, you
will need the following:
\begin{itemize}
- \item the universal ($\forall$) and existential ($\exists$) quantifier
+ \item the universal ($\forall$) and existential ($\exists$) quantifiers
\item the conjunction $\land$
\item the implication $\implies$
\end{itemize}
Moreover, you will need the equality symbol $=$ between two elements of a set
(if $a$ and $b$ are two elements of the same set, ``$a=b$'' is a mathematical
- statement and it is \textbf{true} if and only if they are the same element).
+ statement and it is \textbf{true} if and only if $a$ and $b$ are the same
+ element).
\emph{Warning: your definition must depend on a set $S$ and on a ``variable
statement'' $A(x)$, as the existential and universal quantifiers.}
@@ -107,6 +122,27 @@ here}'' ?
\section{Proofs}
\begin{exercise}
+ Prove by induction that
+ \begin{align*}
+ \forall n\in\mathbb N,\quad \sum_{k=1}^n(2k-1)=n^2
+ \end{align*}
+ (here $\sum_{k=1}^n(2k-1)$ means $1+3+5+\cdots+ (2n-1)$).
+\end{exercise}
+
+\begin{exercise}
+ If $n\in \mathbb N$ the \emph{factorial} of $n$, denoted by $n!$ is defined
+ as follows:
+ \begin{align*}
+ n!=\begin{cases}
+ 1&\text{if } n=0,\\
+ n\times (n-1)! & \text{if } n> 0.
+ \end{cases}
+ \end{align*}
+ Prove by induction that if $n\geq 4$ then $n!\geq 2^n$.
+\end{exercise}
+
+
+\begin{exercise}
Is the following statement true or false? Give a proof of your answer.
\begin{align*}
\forall n\in \mathbb N,\, n^2 -4n +5>n
diff --git a/slides/preplogic-slides.aux b/slides/preplogic-slides.aux
@@ -76,26 +76,26 @@
\@writefile{nav}{\headcommand {\beamer@framepages {42}{42}}}
\@writefile{nav}{\headcommand {\slideentry {4}{0}{3}{43/45}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {43}{45}}}
-\@writefile{nav}{\headcommand {\slideentry {4}{0}{4}{46/46}{}{0}}}
-\@writefile{nav}{\headcommand {\beamer@framepages {46}{46}}}
-\@writefile{toc}{\beamer@sectionintoc {5}{Proofs}{47}{0}{5}}
-\@writefile{nav}{\headcommand {\beamer@sectionpages {40}{46}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {40}{46}}}
-\@writefile{nav}{\headcommand {\sectionentry {5}{Proofs}{47}{Proofs}{0}}}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{1}{47/50}{}{0}}}
-\@writefile{nav}{\headcommand {\beamer@framepages {47}{50}}}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{2}{51/55}{}{0}}}
-\@writefile{nav}{\headcommand {\beamer@framepages {51}{55}}}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{3}{56/57}{}{0}}}
-\@writefile{nav}{\headcommand {\beamer@framepages {56}{57}}}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{4}{58/64}{}{0}}}
-\@writefile{nav}{\headcommand {\beamer@framepages {58}{64}}}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{5}{65/66}{}{0}}}
-\@writefile{nav}{\headcommand {\beamer@framepages {65}{66}}}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{6}{67/71}{}{0}}}
-\@writefile{nav}{\headcommand {\beamer@framepages {67}{71}}}
+\@writefile{toc}{\beamer@sectionintoc {5}{Proofs}{46}{0}{5}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {40}{45}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {40}{45}}}
+\@writefile{nav}{\headcommand {\sectionentry {5}{Proofs}{46}{Proofs}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{1}{46/49}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {46}{49}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{2}{50/54}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {50}{54}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{3}{55/56}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {55}{56}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{4}{57/63}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {57}{63}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{5}{64/65}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {64}{65}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{6}{66/70}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {66}{70}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{7}{71/71}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {71}{71}}}
\@writefile{nav}{\headcommand {\beamer@partpages {1}{71}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {47}{71}}}
-\@writefile{nav}{\headcommand {\beamer@sectionpages {47}{71}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {46}{71}}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {46}{71}}}
\@writefile{nav}{\headcommand {\beamer@documentpages {71}}}
\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {29}}}
diff --git a/slides/preplogic-slides.fdb_latexmk b/slides/preplogic-slides.fdb_latexmk
@@ -1,5 +1,5 @@
# Fdb version 3
-["pdflatex"] 1599409436 "preplogic-slides.tex" "preplogic-slides.pdf" "preplogic-slides" 1599409441
+["pdflatex"] 1599412181 "preplogic-slides.tex" "preplogic-slides.pdf" "preplogic-slides" 1599412185
"/usr/share/texmf-dist/fonts/map/fontname/texfonts.map" 1594687104 3524 cb3e574dea2d1052e39280babc910dc8 ""
"/usr/share/texmf-dist/fonts/map/pdftex/updmap/pdftex.map" 1594687104 4851843 f8aac22e46e9a458223e5c13b1e20998 ""
"/usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1594687104 1004 54797486969f23fa377b128694d548df ""
@@ -204,17 +204,17 @@
"/usr/share/texmf-dist/tex/latex/xcolor/xcolor.sty" 1594687104 55589 34128738f682d033422ca125f82e5d62 ""
"/usr/share/texmf-dist/web2c/texmf.cnf" 1597672114 39446 755423e82e7afb756f49b242a15f4ec2 ""
"/usr/share/texmf-var/web2c/pdftex/pdflatex.fmt" 1598712773 2434818 64d78922a5d2a9baf6bf1beec95a9374 ""
- "preplogic-slides.aux" 1599409440 6068 50b72b0885ae780ffcd7f1e76f21d7ac "pdflatex"
- "preplogic-slides.nav" 1599409440 3672 7a02b80ee1eb79ed6628b6b44b98f41e "pdflatex"
- "preplogic-slides.out" 1599409440 231 deb4a29a1afc0897b65a37cc63a87407 "pdflatex"
- "preplogic-slides.tex" 1599409430 13551 0585e4bf0bb5c04ed9dea539aaf36342 ""
- "preplogic-slides.toc" 1599409440 240 82b64b5af661cb4f9fe5c48ed162b693 "pdflatex"
+ "preplogic-slides.aux" 1599412185 6068 0cd160fad86cda8453c8a27f21ba7a8b "pdflatex"
+ "preplogic-slides.nav" 1599412185 3672 0800028632c9a7b0abd7c91d24b51be9 "pdflatex"
+ "preplogic-slides.out" 1599412185 231 deb4a29a1afc0897b65a37cc63a87407 "pdflatex"
+ "preplogic-slides.tex" 1599412180 14004 9f55841449bbd22b45df126f77402832 ""
+ "preplogic-slides.toc" 1599412185 240 128cdf304ee282775db2a41da35e3a3e "pdflatex"
"unilu.jpg" 1554272896 41957 a77f6a50964dc93c1a7378a3852a421d ""
(generated)
- "preplogic-slides.nav"
"preplogic-slides.toc"
- "preplogic-slides.aux"
- "preplogic-slides.out"
"preplogic-slides.snm"
+ "preplogic-slides.out"
+ "preplogic-slides.aux"
+ "preplogic-slides.nav"
"preplogic-slides.pdf"
"preplogic-slides.log"
diff --git a/slides/preplogic-slides.fls b/slides/preplogic-slides.fls
@@ -449,9 +449,9 @@ INPUT unilu.jpg
INPUT ./unilu.jpg
INPUT unilu.jpg
INPUT ./unilu.jpg
+INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmssbx10.tfm
INPUT unilu.jpg
INPUT ./unilu.jpg
-INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmssbx10.tfm
INPUT unilu.jpg
INPUT ./unilu.jpg
INPUT unilu.jpg
diff --git a/slides/preplogic-slides.log b/slides/preplogic-slides.log
@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/VoidLinux) (preloaded format=pdflatex 2020.8.29) 6 SEP 2020 18:23
+This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/VoidLinux) (preloaded format=pdflatex 2020.8.29) 6 SEP 2020 19:09
entering extended mode
restricted \write18 enabled.
file:line:error style messages enabled.
@@ -977,203 +977,203 @@ Package pdftex.def Info: unilu.jpg used on input line 376.
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 394.
+Package pdftex.def Info: unilu.jpg used on input line 403.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[43
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 394.
+Package pdftex.def Info: unilu.jpg used on input line 403.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[44
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 394.
+Package pdftex.def Info: unilu.jpg used on input line 403.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[45
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 398.
+Package pdftex.def Info: unilu.jpg used on input line 420.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[46
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 415.
+Package pdftex.def Info: unilu.jpg used on input line 420.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[47
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 415.
+Package pdftex.def Info: unilu.jpg used on input line 420.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[48
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 415.
+Package pdftex.def Info: unilu.jpg used on input line 420.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[49
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 415.
+Package pdftex.def Info: unilu.jpg used on input line 441.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[50
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 436.
+Package pdftex.def Info: unilu.jpg used on input line 441.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[51
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 436.
+Package pdftex.def Info: unilu.jpg used on input line 441.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[52
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 436.
+Package pdftex.def Info: unilu.jpg used on input line 441.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[53
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 436.
+Package pdftex.def Info: unilu.jpg used on input line 441.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[54
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 436.
+Package pdftex.def Info: unilu.jpg used on input line 459.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[55
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 454.
+Package pdftex.def Info: unilu.jpg used on input line 459.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[56
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 454.
+Package pdftex.def Info: unilu.jpg used on input line 483.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[57
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 478.
+Package pdftex.def Info: unilu.jpg used on input line 483.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[58
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 478.
+Package pdftex.def Info: unilu.jpg used on input line 483.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[59
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 478.
+Package pdftex.def Info: unilu.jpg used on input line 483.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[60
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 478.
+Package pdftex.def Info: unilu.jpg used on input line 483.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[61
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 478.
+Package pdftex.def Info: unilu.jpg used on input line 483.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[62
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 478.
+Package pdftex.def Info: unilu.jpg used on input line 483.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[63
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 478.
+Package pdftex.def Info: unilu.jpg used on input line 500.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[64
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 495.
+Package pdftex.def Info: unilu.jpg used on input line 500.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[65
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 495.
+Package pdftex.def Info: unilu.jpg used on input line 529.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[66
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 524.
+Package pdftex.def Info: unilu.jpg used on input line 529.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[67
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 524.
+Package pdftex.def Info: unilu.jpg used on input line 529.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[68
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 524.
+Package pdftex.def Info: unilu.jpg used on input line 529.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[69
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 524.
+Package pdftex.def Info: unilu.jpg used on input line 529.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[70
]
File: unilu.jpg Graphic file (type jpg)
<use unilu.jpg>
-Package pdftex.def Info: unilu.jpg used on input line 524.
+Package pdftex.def Info: unilu.jpg used on input line 540.
(pdftex.def) Requested size: 41.93689pt x 37.58171pt.
[71
@@ -1187,11 +1187,11 @@ Package pdftex.def Info: unilu.jpg used on input line 524.
\tf@snm=\write8
\openout8 = `preplogic-slides.snm'.
-Package atveryend Info: Empty hook `BeforeClearDocument' on input line 526.
-Package atveryend Info: Empty hook `AfterLastShipout' on input line 526.
+Package atveryend Info: Empty hook `BeforeClearDocument' on input line 543.
+Package atveryend Info: Empty hook `AfterLastShipout' on input line 543.
(./preplogic-slides.aux)
-Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 526.
-Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 526.
+Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 543.
+Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 543.
Package rerunfilecheck Info: File `preplogic-slides.out' has not changed.
(rerunfilecheck) Checksum: DEB4A29A1AFC0897B65A37CC63A87407;231.
@@ -1202,13 +1202,13 @@ LaTeX Font Warning: Some font shapes were not available, defaults substituted.
Here is how much of TeX's memory you used:
18146 strings out of 480478
343117 string characters out of 5905927
- 607445 words of memory out of 5000000
+ 607433 words of memory out of 5000000
33570 multiletter control sequences out of 15000+600000
545011 words of font info for 70 fonts, out of 8000000 for 9000
1141 hyphenation exceptions out of 8191
- 54i,20n,63p,800b,908s stack positions out of 5000i,500n,10000p,200000b,80000s
+ 54i,20n,64p,800b,908s stack positions out of 5000i,500n,10000p,200000b,80000s
</usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmss10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmss12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmss17.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmss8.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmss9.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmssbx10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmssi10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmssi8.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmssi9.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy9.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb>
-Output written on preplogic-slides.pdf (71 pages, 363451 bytes).
+Output written on preplogic-slides.pdf (71 pages, 364862 bytes).
PDF statistics:
2027 PDF objects out of 2073 (max. 8388607)
1904 compressed objects within 20 object streams
diff --git a/slides/preplogic-slides.nav b/slides/preplogic-slides.nav
@@ -54,25 +54,25 @@
\headcommand {\beamer@framepages {42}{42}}
\headcommand {\slideentry {4}{0}{3}{43/45}{}{0}}
\headcommand {\beamer@framepages {43}{45}}
-\headcommand {\slideentry {4}{0}{4}{46/46}{}{0}}
-\headcommand {\beamer@framepages {46}{46}}
-\headcommand {\beamer@sectionpages {40}{46}}
-\headcommand {\beamer@subsectionpages {40}{46}}
-\headcommand {\sectionentry {5}{Proofs}{47}{Proofs}{0}}
-\headcommand {\slideentry {5}{0}{1}{47/50}{}{0}}
-\headcommand {\beamer@framepages {47}{50}}
-\headcommand {\slideentry {5}{0}{2}{51/55}{}{0}}
-\headcommand {\beamer@framepages {51}{55}}
-\headcommand {\slideentry {5}{0}{3}{56/57}{}{0}}
-\headcommand {\beamer@framepages {56}{57}}
-\headcommand {\slideentry {5}{0}{4}{58/64}{}{0}}
-\headcommand {\beamer@framepages {58}{64}}
-\headcommand {\slideentry {5}{0}{5}{65/66}{}{0}}
-\headcommand {\beamer@framepages {65}{66}}
-\headcommand {\slideentry {5}{0}{6}{67/71}{}{0}}
-\headcommand {\beamer@framepages {67}{71}}
+\headcommand {\beamer@sectionpages {40}{45}}
+\headcommand {\beamer@subsectionpages {40}{45}}
+\headcommand {\sectionentry {5}{Proofs}{46}{Proofs}{0}}
+\headcommand {\slideentry {5}{0}{1}{46/49}{}{0}}
+\headcommand {\beamer@framepages {46}{49}}
+\headcommand {\slideentry {5}{0}{2}{50/54}{}{0}}
+\headcommand {\beamer@framepages {50}{54}}
+\headcommand {\slideentry {5}{0}{3}{55/56}{}{0}}
+\headcommand {\beamer@framepages {55}{56}}
+\headcommand {\slideentry {5}{0}{4}{57/63}{}{0}}
+\headcommand {\beamer@framepages {57}{63}}
+\headcommand {\slideentry {5}{0}{5}{64/65}{}{0}}
+\headcommand {\beamer@framepages {64}{65}}
+\headcommand {\slideentry {5}{0}{6}{66/70}{}{0}}
+\headcommand {\beamer@framepages {66}{70}}
+\headcommand {\slideentry {5}{0}{7}{71/71}{}{0}}
+\headcommand {\beamer@framepages {71}{71}}
\headcommand {\beamer@partpages {1}{71}}
-\headcommand {\beamer@subsectionpages {47}{71}}
-\headcommand {\beamer@sectionpages {47}{71}}
+\headcommand {\beamer@subsectionpages {46}{71}}
+\headcommand {\beamer@sectionpages {46}{71}}
\headcommand {\beamer@documentpages {71}}
\headcommand {\gdef \inserttotalframenumber {29}}
diff --git a/slides/preplogic-slides.pdf b/slides/preplogic-slides.pdf
Binary files differ.
diff --git a/slides/preplogic-slides.synctex.gz b/slides/preplogic-slides.synctex.gz
Binary files differ.
diff --git a/slides/preplogic-slides.tex b/slides/preplogic-slides.tex
@@ -350,7 +350,7 @@ Mathematician: ``Yes.''
\begin{itemize}
\item \textbf{Universal quantifier} ($\forall$ or ``for all''):
- ``$\forall x\in S,\,A(x)$'' means that if we replace $x$ with any
+ ``$\forall x\in S,\,A(x)$'' means that if we replace ``$x$'' with any
element of $S$, $A(x)$ is always \textbf{true}.
\item \textbf{Existential quantifier} ($\exists$ or ``there exists''):
``$\exists x\in S,\, A(x)$'' means that $A(x)$ is \textbf{true} for
@@ -385,16 +385,21 @@ Mathematician: ``Yes.''
\neg(\exists x\in S,\, A(x))&=\only<1-2>{\quad?}
\onslide<3->{\forall x\in S,\,\neg A(x)}\\
\end{align*}
- \pause
+ \onslide<2->{
\begin{example}
\begin{center}
$\neg$``every number is even'' = ``there is at least one odd number''
\end{center}
\end{example}
-\end{frame}
-
-\begin{frame}
- (exercise)
+ }
+ \onslide<3->{
+ \begin{example}
+ \begin{center}
+ $\neg$``$\exists x\in \mathbb N,\, x+3=9$'' =
+ ``$\forall x\in \mathbb N,\, x+3\neq 9$''
+ \end{center}
+ \end{example}
+ }
\end{frame}
\section{Proofs}
@@ -523,4 +528,16 @@ Mathematician: ``Yes.''
\end{proof}
\end{frame}
+\begin{frame}{The end}
+ What you have learned in this course:
+ \begin{itemize}
+ \item Basic logic operations and logic implication
+ \item Quantifiers and \textbf{their negation}
+ \item Some basic mathematical proofs
+ \end{itemize}
+ \vspace{10pt}
+ \refgithub
+\end{frame}
+
+
\end{document}
diff --git a/slides/preplogic-slides.toc b/slides/preplogic-slides.toc
@@ -2,4 +2,4 @@
\beamer@sectionintoc {2}{Logical operations}{11}{0}{2}
\beamer@sectionintoc {3}{Implication}{28}{0}{3}
\beamer@sectionintoc {4}{Quantifiers}{40}{0}{4}
-\beamer@sectionintoc {5}{Proofs}{47}{0}{5}
+\beamer@sectionintoc {5}{Proofs}{46}{0}{5}
