From 4ca009f025a29351bcf1160cd68d513f04687713 Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Sun, 6 Sep 2020 18:04:41 +0200 Subject: First commit --- exercises/preplogic-exercises.aux | 5 + exercises/preplogic-exercises.fdb_latexmk | 62 ++++++++++++ exercises/preplogic-exercises.fls | 85 +++++++++++++++++ exercises/preplogic-exercises.log | 151 ++++++++++++++++++++++++++++++ exercises/preplogic-exercises.pdf | Bin 0 -> 125146 bytes exercises/preplogic-exercises.synctex.gz | Bin 0 -> 12003 bytes exercises/preplogic-exercises.tex | 123 ++++++++++++++++++++++++ 7 files changed, 426 insertions(+) create mode 100644 exercises/preplogic-exercises.aux create mode 100644 exercises/preplogic-exercises.fdb_latexmk create mode 100644 exercises/preplogic-exercises.fls create mode 100644 exercises/preplogic-exercises.log create mode 100644 exercises/preplogic-exercises.pdf create mode 100644 exercises/preplogic-exercises.synctex.gz create mode 100644 exercises/preplogic-exercises.tex (limited to 'exercises') diff --git a/exercises/preplogic-exercises.aux b/exercises/preplogic-exercises.aux new file mode 100644 index 0000000..c375d33 --- /dev/null +++ b/exercises/preplogic-exercises.aux @@ -0,0 +1,5 @@ +\relax +\@writefile{toc}{\contentsline {section}{\numberline {1}Logical operations}{1}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {2}Implication}{1}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {3}Quantifiers}{2}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {4}Proofs}{2}\protected@file@percent } diff --git a/exercises/preplogic-exercises.fdb_latexmk b/exercises/preplogic-exercises.fdb_latexmk new file mode 100644 index 0000000..c0a94f2 --- /dev/null +++ b/exercises/preplogic-exercises.fdb_latexmk @@ -0,0 +1,62 @@ +# Fdb version 3 +["pdflatex"] 1599407243 "preplogic-exercises.tex" "preplogic-exercises.pdf" "preplogic-exercises" 1599407243 + "/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 "" + "/usr/share/texmf-dist/fonts/tfm/jknappen/ec/tcrm1000.tfm" 1594687104 1536 e07581a4bb3136ece9eeb4c3ffab8233 "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1594687104 1004 54797486969f23fa377b128694d548df "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1594687104 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1594687104 916 f87d7c45f9c908e672703b83b72241a3 "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm" 1594687104 924 9904cf1d39e9767e7a3622f2a125a565 "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1594687104 928 2dc8d444221b7a635bb58038579b861a "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1594687104 908 2921f8a10601f252058503cc6570e581 "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm" 1594687104 940 75ac932a52f80982a9f8ea75d03a34cf "" + "/usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1594687104 940 228d6584342e91276bf566bcf9716b83 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm" 1594687104 1328 c834bbb027764024c09d3d2bf908b5f0 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm" 1594687104 1324 c910af8c371558dc20f2d7822f66fe64 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmex10.tfm" 1594687104 992 662f679a0b3d2d53c1b94050fdaa3f50 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm" 1594687104 1524 4414a8315f39513458b80dfc63bff03a "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm" 1594687104 1512 f21f83efb36853c0b70002322c1ab3ad "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm" 1594687104 1520 eccf95517727cb11801f4f1aee3a21b4 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm" 1594687104 1288 655e228510b4c2a1abe905c368440826 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr17.tfm" 1594687104 1292 296a67155bdbfc32aa9c636f21e91433 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr6.tfm" 1594687104 1300 b62933e007d01cfd073f79b963c01526 "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr8.tfm" 1594687104 1292 21c1c5bfeaebccffdb478fd231a0997d "" + "/usr/share/texmf-dist/fonts/tfm/public/cm/cmsy10.tfm" 1594687104 1124 6c73e740cf17375f03eec0ee63599741 "" + "/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/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/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/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/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/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 "" + "/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd" 1594687104 961 6518c6525a34feb5e8250ffa91731cff "" + "/usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd" 1594687104 961 d02606146ba5601b5645f987c92e6193 "" + "/usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1594687104 2211 ca7ce284ab93c8eecdc6029dc5ccbd73 "" + "/usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty" 1594687104 4161 7f6eb9092061a11f87d08ed13515b48d "" + "/usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty" 1594687104 85660 baee036978c7a91f4e2bba43f05e5945 "" + "/usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty" 1594687104 4116 32e6abd27229755a83a8b7f18e583890 "" + "/usr/share/texmf-dist/tex/latex/amsmath/amstext.sty" 1594687104 2432 8ff93b1137020e8f21930562a874ae66 "" + "/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/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 "" + (generated) + "preplogic-exercises.log" + "preplogic-exercises.pdf" + "preplogic-exercises.aux" diff --git a/exercises/preplogic-exercises.fls b/exercises/preplogic-exercises.fls new file mode 100644 index 0000000..2dcc725 --- /dev/null +++ b/exercises/preplogic-exercises.fls @@ -0,0 +1,85 @@ +PWD /home/sebastiano/Dropbox/teaching/preparatory_logic/exercises +INPUT /usr/share/texmf-dist/web2c/texmf.cnf +INPUT /usr/share/texmf-var/web2c/pdftex/pdflatex.fmt +INPUT preplogic-exercises.tex +OUTPUT preplogic-exercises.log +INPUT /usr/share/texmf-dist/tex/latex/base/article.cls +INPUT /usr/share/texmf-dist/tex/latex/base/article.cls +INPUT /usr/share/texmf-dist/tex/latex/base/size10.clo +INPUT /usr/share/texmf-dist/tex/latex/base/size10.clo +INPUT /usr/share/texmf-dist/tex/latex/base/inputenc.sty +INPUT /usr/share/texmf-dist/tex/latex/base/inputenc.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amstext.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT /usr/share/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texmf-dist/tex/latex/amscls/amsthm.sty +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/l3backend/l3backend-pdfmode.def +INPUT /usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def +INPUT preplogic-exercises.aux +INPUT preplogic-exercises.aux +OUTPUT preplogic-exercises.aux +INPUT /usr/share/texmf-dist/fonts/map/fontname/texfonts.map +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr17.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr8.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr6.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmsy10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmex10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd +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/cmr12.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.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/amsfonts/symbols/msbm5.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmti10.tfm +OUTPUT preplogic-exercises.pdf +INPUT /usr/share/texmf-dist/fonts/map/pdftex/updmap/pdftex.map +INPUT /usr/share/texmf-dist/fonts/tfm/jknappen/ec/tcrm1000.tfm +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/cmmi10.pfb +INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi5.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/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 new file mode 100644 index 0000000..340c2da --- /dev/null +++ b/exercises/preplogic-exercises.log @@ -0,0 +1,151 @@ +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 +entering extended mode + restricted \write18 enabled. + file:line:error style messages enabled. + %&-line parsing enabled. +**preplogic-exercises.tex +(./preplogic-exercises.tex +LaTeX2e <2020-02-02> patch level 5 +L3 programming layer <2020-06-03> (/usr/share/texmf-dist/tex/latex/base/article.cls +Document Class: article 2019/12/20 v1.4l Standard LaTeX document class +(/usr/share/texmf-dist/tex/latex/base/size10.clo +File: size10.clo 2019/12/20 v1.4l Standard LaTeX file (size option) +) +\c@part=\count167 +\c@section=\count168 +\c@subsection=\count169 +\c@subsubsection=\count170 +\c@paragraph=\count171 +\c@subparagraph=\count172 +\c@figure=\count173 +\c@table=\count174 +\abovecaptionskip=\skip47 +\belowcaptionskip=\skip48 +\bibindent=\dimen134 +) (/usr/share/texmf-dist/tex/latex/base/inputenc.sty +Package: inputenc 2018/08/11 v1.3c Input encoding file +\inpenc@prehook=\toks15 +\inpenc@posthook=\toks16 +) (/usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2020/01/20 v2.17e AMS math features +\@mathmargin=\skip49 + +For additional information on amsmath, use the `?' option. +(/usr/share/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 AMS text + (/usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 generic functions +\@emptytoks=\toks17 +\ex@=\dimen135 +)) (/usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d Bold Symbols +\pmbraise@=\dimen136 +) (/usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 2016/03/08 v2.02 operator names +) +\inf@bad=\count175 +LaTeX Info: Redefining \frac on input line 227. +\uproot@=\count176 +\leftroot@=\count177 +LaTeX Info: Redefining \overline on input line 389. +\classnum@=\count178 +\DOTSCASE@=\count179 +LaTeX Info: Redefining \ldots on input line 486. +LaTeX Info: Redefining \dots on input line 489. +LaTeX Info: Redefining \cdots on input line 610. +\Mathstrutbox@=\box45 +\strutbox@=\box46 +\big@size=\dimen137 +LaTeX Font Info: Redeclaring font encoding OML on input line 733. +LaTeX Font Info: Redeclaring font encoding OMS on input line 734. +\macc@depth=\count180 +\c@MaxMatrixCols=\count181 +\dotsspace@=\muskip16 +\c@parentequation=\count182 +\dspbrk@lvl=\count183 +\tag@help=\toks18 +\row@=\count184 +\column@=\count185 +\maxfields@=\count186 +\andhelp@=\toks19 +\eqnshift@=\dimen138 +\alignsep@=\dimen139 +\tagshift@=\dimen140 +\tagwidth@=\dimen141 +\totwidth@=\dimen142 +\lineht@=\dimen143 +\@envbody=\toks20 +\multlinegap=\skip50 +\multlinetaggap=\skip51 +\mathdisplay@stack=\toks21 +LaTeX Info: Redefining \[ on input line 2859. +LaTeX Info: Redefining \] on input line 2860. +) (/usr/share/texmf-dist/tex/latex/amscls/amsthm.sty +Package: amsthm 2020/05/29 v2.20.6 +\thm@style=\toks22 +\thm@bodyfont=\toks23 +\thm@headfont=\toks24 +\thm@notefont=\toks25 +\thm@headpunct=\toks26 +\thm@preskip=\skip52 +\thm@postskip=\skip53 +\thm@headsep=\skip54 +\dth@everypar=\toks27 +) (/usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols + (/usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +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. +)) +\c@exercise=\count187 + (/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__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 +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. + (/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 + 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} +Output written on preplogic-exercises.pdf (2 pages, 125146 bytes). +PDF statistics: + 60 PDF objects out of 1000 (max. 8388607) + 43 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 new file mode 100644 index 0000000..7db8e9f Binary files /dev/null and b/exercises/preplogic-exercises.pdf differ diff --git a/exercises/preplogic-exercises.synctex.gz b/exercises/preplogic-exercises.synctex.gz new file mode 100644 index 0000000..1a25b1d Binary files /dev/null and b/exercises/preplogic-exercises.synctex.gz differ diff --git a/exercises/preplogic-exercises.tex b/exercises/preplogic-exercises.tex new file mode 100644 index 0000000..cd37db7 --- /dev/null +++ b/exercises/preplogic-exercises.tex @@ -0,0 +1,123 @@ +\documentclass[a4paper,oneside]{article} +\usepackage[utf8]{inputenc} +\usepackage{amsmath} +\usepackage{amsthm} +\usepackage{amssymb} + +\theoremstyle{definition} \newtheorem{exercise}{Exercise}[section] + +\author{Sebastiano Tronto (uni.lu)} +\title{Elementary logic exercises (Prep Camp 2020)} + +\begin{document} +\maketitle + +\section{Logical operations} + +\begin{exercise} + Determine if the following statement are \textbf{true} or \textbf{false}: + \begin{enumerate} + \item ``Today is Tuesday or Germany has more inhabitants than Luxembourg'' + \item ``$7$ is odd and $2+2=5$'' + \item Every number of the form $2^{2^n}+1$, for $n=1,2,3...$, is prime. + \end{enumerate} +\end{exercise} + +\begin{exercise} + What is the negation of the sentence ``\emph{I payed attention in class and I + did not do my homework}'' ? +\end{exercise} + +\begin{exercise} + Simplify the following logical expressions using the properties of logical + operations (where $A,B$ and $C$ are statements): + \begin{enumerate} + \item $A\land(A\lor B)$ + \item $A\lor (B\land A)$ + \item $(A\lor B) \land \neg A$ + \item $A \lor (\neg A\land B)$ + \item $(\neg (A\lor \neg B))\land ((A\lor C) \land \neg C)$ + \end{enumerate} +\end{exercise} + +\section{Implication} + +\begin{exercise} + Fill in the following truth table: + \begin{align*} + \begin{array}{|c|c|c|c|c|} + \hline + A & B & C & \neg(A\implies B) & (A\implies B) \implies C \\ + \hline + 0 & 0 & 0 & & \\ + \hline + 0 & 0 & 1 & & \\ + \hline + 0 & 1 & 0 & & \\ + \hline + 0 & 1 & 1 & & \\ + \hline + 1 & 0 & 0 & & \\ + \hline + 1 & 0 & 1 & & \\ + \hline + 1 & 1 & 0 & & \\ + \hline + 1 & 1 & 1 & & \\ + \hline + \end{array} + \end{align*} +\end{exercise} + +\begin{exercise}[Transitivity] + Prove that the following statement is true for any statements $A,B$ and $C$: + \begin{align*} + ((A\implies B)\land (B\implies C))\implies (A\implies C) + \end{align*} +\end{exercise} + +\begin{exercise} +What is the contrapositive of ``\emph{If this table is not reserved, we sit +here}'' ? +\end{exercise} + +\section{Quantifiers} + +\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 ``$\exists!x\in \mathbb N,\,x+2=5$. + 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 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). + + \emph{Warning: your definition must depend on a set $S$ and on a ``variable + statement'' $A(x)$, as the existential and universal quantifiers.} +\end{exercise} + +\section{Proofs} + +\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 + \end{align*} +\end{exercise} + +\begin{exercise} + Do the last point of Exercise 1.1 again, but this time give a proof of your + answer. +\end{exercise} + + + +\end{document} -- cgit v1.3