finally finished hw1 lol

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 ""
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@@ -35,6 +35,7 @@
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   "/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 @@
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   "/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 ""
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   "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1654720880 2222 78b930a5a6e3dc2ac69b78c2057b94d7 ""
@@ -140,8 +142,8 @@
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   "/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.aux" 1696023089 194 99cff90ccc1d8836afe187a548b2e38e "pdflatex"
-  "hw1.tex" 1694145543 6845 6f0a9d7413c773083ce767950272b7e1 ""
+  "hw1.tex" 1696023088 8571 848f96e4db99853e25d2c2e5a076b0ea ""
   (generated)
   "hw1.aux"
   "hw1.log"

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/amsfonts/amssymb.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/amscls/amsthm.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.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/amscls/amsthm.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.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/amscls/amsthm.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.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/amscls/amsthm.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.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/amscls/amsthm.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
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 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
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 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

hw/hw1/hw1.log

@@ -1,10 +1,10 @@
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+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/hw1.tex
-(/home/rushil/school/math/hw/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
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 \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
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+ (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty
+Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
+\symAMSa=\mathgroup4
+\symAMSb=\mathgroup5
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+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
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 \thm@style=\toks22
 \thm@bodyfont=\toks23
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 \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
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 \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:    Checking defaults for OML/cmm/m/it on input line 136.
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+LaTeX Font Info:    ... okay on input line 136.
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-LaTeX Font Info:    ... okay on input line 135.
+LaTeX Font Info:    ... okay on input line 136.
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+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 136.
-LaTeX Font Info:    ... okay on input line 135.
+LaTeX Font Info:    ... okay on input line 136.
-LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 135.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 136.
-LaTeX Font Info:    ... okay on input line 135.
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-LaTeX Font Info:    ... okay on input line 135.
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+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 136.
-LaTeX Font Info:    ... okay on input line 135.
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-LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 135.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 136.
-LaTeX Font Info:    ... okay on input line 135.
+LaTeX Font Info:    ... okay on input line 136.
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 [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
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 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.
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 File: umsa.fd 2013/01/14 v3.01 AMS symbols A
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+LaTeX Font Info:    Trying to load font information for U+msb on input line 138.
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 File: umsb.fd 2013/01/14 v3.01 AMS symbols B
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 Here is how much of TeX's memory you used:
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+ 318208 string characters out of 5794081
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+ 1870330 words of memory out of 5000000
- 35323 multiletter control sequences out of 15000+600000
+ 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
+ 102i,11n,104p,445b,261s stack positions out of 10000i,1000n,20000p,200000b,200000s
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+</usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr9.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb>
-Output written on hw1.pdf (4 pages, 103380 bytes).
+Output written on hw1.pdf (4 pages, 114911 bytes).
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+ 65 PDF objects out of 1000 (max. 8388607)
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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{6}\\
-\problem{8}
+Use a truth table to verify the first De Morgan law
-\textbf{a)}
+\begin{displaymath}
-\textbf{b)}
+    \neg(p \wedge q) \equiv \neg p \vee \neg q
-\prob{32}
+\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