mirror of
https://github.com/Rushilwiz/math381.git
synced 2025-04-03 19:30:16 -04:00
finally finished hw1 lol
This commit is contained in:
parent
5f52fecc0d
commit
2d5e7e7ae6
|
|
@ -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"
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -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
|
||||
</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>
|
||||
Output written on hw1.pdf (4 pages, 103380 bytes).
|
||||
102i,11n,104p,445b,261s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
||||
</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, 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)
|
||||
|
||||
|
|
|
|||
BIN
hw/hw1/hw1.pdf
BIN
hw/hw1/hw1.pdf
Binary file not shown.
Binary file not shown.
|
|
@ -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
|
||||
|
||||
|
|
|
|||
BIN
mt1_formula_sheet.pdf
Normal file
BIN
mt1_formula_sheet.pdf
Normal file
Binary file not shown.
Loading…
Reference in New Issue
Block a user