diff --git a/hw/hw1/hw1.fdb_latexmk b/hw/hw1/hw1.fdb_latexmk index 17dc6b5..f69d1a8 100644 --- a/hw/hw1/hw1.fdb_latexmk +++ b/hw/hw1/hw1.fdb_latexmk @@ -1,7 +1,7 @@ # Fdb version 4 -["pdflatex"] 1694145544 "/home/rushil/school/math/hw/hw1.tex" "hw1.pdf" "hw1" 1694145544 0 +["pdflatex"] 1696023088 "/home/rushil/school/math/hw/hw1/hw1.tex" "hw1.pdf" "hw1" 1696023089 0 "/etc/texmf/web2c/texmf.cnf" 1693368362 475 c0e671620eb5563b2130f56340a5fde8 "" - "/home/rushil/school/math/hw/hw1.tex" 1694145543 6845 6f0a9d7413c773083ce767950272b7e1 "" + "/home/rushil/school/math/hw/hw1/hw1.tex" 1696023088 8571 848f96e4db99853e25d2c2e5a076b0ea "" "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" @@ -35,6 +35,7 @@ "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb" 1248133631 37944 359e864bd06cde3b1cf57bb20757fb06 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti12.pfb" 1248133631 36118 fad905eba93cff5bce1e185fe980a177 "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb" 1248133631 31764 459c573c03a4949a528c2cc7f557e217 "" "/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1461363279 71627 94eb9990bed73c364d7f53f960cc8c5b "" "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex" 1673816307 1016 1c2b89187d12a2768764b83b4945667c "" "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex" 1601326656 43820 1fef971b75380574ab35a0d37fd92608 "" @@ -97,6 +98,7 @@ "/usr/share/texlive/texmf-dist/tex/latex/algorithms/algorithm.sty" 1251330371 3249 15763257e50278eef5db1952ccde229c "" "/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty" 1591045760 12594 0d51ac3a545aaaa555021326ff22a6cc "" "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1359763108 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" + "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1359763108 13829 94730e64147574077f8ecfea9bb69af4 "" "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd" 1359763108 961 6518c6525a34feb5e8250ffa91731cff "" "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd" 1359763108 961 d02606146ba5601b5645f987c92e6193 "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1654720880 2222 78b930a5a6e3dc2ac69b78c2057b94d7 "" @@ -140,8 +142,8 @@ "/usr/share/texmf/web2c/texmf.cnf" 1681034085 39561 34c98e380bf7c7201ee6a7909aff625a "" "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1693368379 4623455 fa0568a71dd9a288d6c226ee477506c6 "" "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1693368408 7880218 5644a8bb2704ddc1060e0c139ce5389a "" - "hw1.aux" 1694145544 194 99cff90ccc1d8836afe187a548b2e38e "pdflatex" - "hw1.tex" 1694145543 6845 6f0a9d7413c773083ce767950272b7e1 "" + "hw1.aux" 1696023089 194 99cff90ccc1d8836afe187a548b2e38e "pdflatex" + "hw1.tex" 1696023088 8571 848f96e4db99853e25d2c2e5a076b0ea "" (generated) "hw1.aux" "hw1.log" diff --git a/hw/hw1/hw1.fls b/hw/hw1/hw1.fls index 68cbf90..4dd579e 100644 --- a/hw/hw1/hw1.fls +++ b/hw/hw1/hw1.fls @@ -1,9 +1,9 @@ -PWD /home/rushil/school/math/hw +PWD /home/rushil/school/math/hw/hw1 INPUT /etc/texmf/web2c/texmf.cnf INPUT /usr/share/texmf/web2c/texmf.cnf INPUT /usr/share/texlive/texmf-dist/web2c/texmf.cnf INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt -INPUT /home/rushil/school/math/hw/hw1.tex +INPUT /home/rushil/school/math/hw/hw1/hw1.tex OUTPUT hw1.log INPUT /usr/share/texlive/texmf-dist/tex/latex/base/article.cls INPUT /usr/share/texlive/texmf-dist/tex/latex/base/article.cls @@ -101,17 +101,17 @@ INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty -INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty @@ -123,6 +123,18 @@ INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty INPUT /usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty @@ -597,3 +609,4 @@ INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr9.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti12.pfb +INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb diff --git a/hw/hw1/hw1.log b/hw/hw1/hw1.log index 9d0cdce..0b1644a 100644 --- a/hw/hw1/hw1.log +++ b/hw/hw1/hw1.log @@ -1,10 +1,10 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2023.8.30) 7 SEP 2023 23:59 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2023.8.30) 29 SEP 2023 17:31 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. %&-line parsing enabled. -**/home/rushil/school/math/hw/hw1.tex -(/home/rushil/school/math/hw/hw1.tex +**/home/rushil/school/math/hw/hw1/hw1.tex +(/home/rushil/school/math/hw/hw1/hw1.tex LaTeX2e <2022-11-01> patch level 1 L3 programming layer <2023-01-16> (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2022/07/02 v1.4n Standard LaTeX document class @@ -100,7 +100,16 @@ LaTeX Info: Redefining \Relbar on input line 971. \mathdisplay@stack=\toks21 LaTeX Info: Redefining \[ on input line 2953. LaTeX Info: Redefining \] on input line 2954. -) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty +) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols + (/usr/share/texlive/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. +)) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty Package: amsthm 2020/05/29 v2.20.6 \thm@style=\toks22 \thm@bodyfont=\toks23 @@ -111,13 +120,6 @@ Package: amsthm 2020/05/29 v2.20.6 \thm@postskip=\skip63 \thm@headsep=\skip64 \dth@everypar=\toks27 -) (/usr/share/texlive/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. ) (/usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty (/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty (/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty (/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex \pgfutil@everybye=\toks28 \pgfutil@tempdima=\dimen150 @@ -435,20 +437,20 @@ File: l3backend-pdftex.def 2023-01-16 L3 backend support: PDF output (pdfTeX) ) (./hw1.aux) \openout1 = `hw1.aux'. -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 135. -LaTeX Font Info: ... okay on input line 135. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 135. -LaTeX Font Info: ... okay on input line 135. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 135. -LaTeX Font Info: ... okay on input line 135. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 135. -LaTeX Font Info: ... okay on input line 135. -LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 135. -LaTeX Font Info: ... okay on input line 135. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 135. -LaTeX Font Info: ... okay on input line 135. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 135. -LaTeX Font Info: ... okay on input line 135. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 136. +LaTeX Font Info: ... okay on input line 136. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 136. +LaTeX Font Info: ... okay on input line 136. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 136. +LaTeX Font Info: ... okay on input line 136. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 136. +LaTeX Font Info: ... okay on input line 136. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 136. +LaTeX Font Info: ... okay on input line 136. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 136. +LaTeX Font Info: ... okay on input line 136. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 136. +LaTeX Font Info: ... okay on input line 136. (/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] \scratchcounter=\count310 @@ -468,29 +470,29 @@ Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 48 (/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live )) -LaTeX Font Info: Trying to load font information for U+msa on input line 137. +LaTeX Font Info: Trying to load font information for U+msa on input line 138. (/usr/share/texlive/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 137. +LaTeX Font Info: Trying to load font information for U+msb on input line 138. (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) [1 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] [3] [4] (./hw1.aux) ) Here is how much of TeX's memory you used: - 15210 strings out of 476091 - 313729 string characters out of 5794081 - 1861330 words of memory out of 5000000 - 35323 multiletter control sequences out of 15000+600000 + 15629 strings out of 476091 + 318208 string characters out of 5794081 + 1870330 words of memory out of 5000000 + 35739 multiletter control sequences out of 15000+600000 521449 words of font info for 67 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 102i,11n,104p,441b,261s stack positions out of 10000i,1000n,20000p,200000b,200000s - -Output written on hw1.pdf (4 pages, 103380 bytes). + 102i,11n,104p,445b,261s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on hw1.pdf (4 pages, 114911 bytes). PDF statistics: - 60 PDF objects out of 1000 (max. 8388607) - 37 compressed objects within 1 object stream + 65 PDF objects out of 1000 (max. 8388607) + 40 compressed objects within 1 object stream 0 named destinations out of 1000 (max. 500000) 13 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/hw/hw1/hw1.pdf b/hw/hw1/hw1.pdf index 8cfe126..464973a 100644 Binary files a/hw/hw1/hw1.pdf and b/hw/hw1/hw1.pdf differ diff --git a/hw/hw1/hw1.synctex.gz b/hw/hw1/hw1.synctex.gz index a697704..f4b61cd 100644 Binary files a/hw/hw1/hw1.synctex.gz and b/hw/hw1/hw1.synctex.gz differ diff --git a/hw/hw1/hw1.tex b/hw/hw1/hw1.tex index 6f90cba..5677481 100644 --- a/hw/hw1/hw1.tex +++ b/hw/hw1/hw1.tex @@ -3,6 +3,7 @@ \usepackage{fancyhdr} \usepackage{extramarks} \usepackage{amsmath} +\usepackage{amssymb} \usepackage{amsthm} \usepackage{amsfonts} \usepackage{tikz} @@ -216,12 +217,47 @@ Express each of these propositions as an English sentence. \\ Since the columns are identical the law is true. -\problem{6} -\problem{8} -\textbf{a)} -\textbf{b)} -\prob{32} +\problem{6}\\ +Use a truth table to verify the first De Morgan law +\begin{displaymath} + \neg(p \wedge q) \equiv \neg p \vee \neg q +\end{displaymath} +\begin{displaymath} + \begin{array}{|c c|c|c|c|c|c|} + p & q & \neg p & \neg q & p \wedge q & \neg(p \wedge q) & \neg p \vee \neg q \\ + \hline + T & T & F & F & T & F & F \\ + T & F & F & T & F & T & T \\ + F & T & T & F & F & T & T \\ + F & F & T & T & F & T & T \\ + \end{array} +\end{displaymath} +\problem{8}\\ +Use De Morgan’s laws to find the negation of each of the +following statements.\\ +\textbf{a)} +Kwame will take a job in industry or go to graduate school. \\ +Kwame will not take a job in the industry and will not go to graduate school.\\ +\textbf{b)} +Yoshiko knows Java and calculus.\\ +Yoshiko does not know Joava or does not know calculus.\\ +\prob{32}\\ +Show that \(p \leftrightarrow q\) and \(\neg p \leftrightarrow \neg q\) are logically equivalent. +\begin{displaymath} + \begin{array}{|c c|c|c|c|c|c|} + + p & q & \neg p & \neg q & p \leftrightarrow q & \neg p \leftrightarrow \neg q \\ + \hline + T & T & F & F & T & T \\ + T & F & F & T & F & F \\ + F & T & T & F & F & F \\ + F & F & T & T & T & T \\ + \end{array} +\end{displaymath} +\begin{align*} + \therefore p \leftrightarrow q \equiv \neg p \leftrightarrow \neg q +\end{align*} \pagebreak diff --git a/mt1_formula_sheet.pdf b/mt1_formula_sheet.pdf new file mode 100644 index 0000000..9943a5e Binary files /dev/null and b/mt1_formula_sheet.pdf differ