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':pL1[`DNen { "1.0_:_Introduction_to_the_Basic_Language_of_Mathematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.1:_Compound_Statements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.2:_More_on_Logical_Statements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.3:_Arguments" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.E:_Basic_Language_of_Mathematics_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1:_Basic_Language_of_Mathematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2:_Basic_Concepts_of_Sets" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3:_Number_Patterns" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4:_Basic_Concepts_of_Euclidean_Geometry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5:_Basic_Concepts_of_Probability" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6:_Introduction_to_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7:_Rational_Reasoning" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "compound statements", "tautology", "authorname:thangarajahp", "calcplot:yes", "jupyter:python", "license:ccbyncsa", "showtoc:yes" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FMount_Royal_University%2FMATH_1150%253A_Mathematical_Reasoning%2F1%253A_Basic_Language_of_Mathematics%2F1.1%253A_Compound_Statements, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), We can make a new statement from other statements; we call these. @m^I;%.I5C2UPG^#Cq/-EXR'G$C'Xnq_@U:tcD1dW+1I$^QuT^gE`u4#lqYg(gVfHr]>W14YXQT)Vk[f?4>5:ViO]M]&&*eMM)d$D!L`*Ld'AjR?FVgE)FUHFb4*>ra-/1Yh A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" Which of the following statement is a proposition? ]gJd]PPOGjD3^B]@ ET (T11(2k0VUbW&qo&P).77K92,YLr;Q68]VG5K&+JEKQ(/K)^=a4m+*(l0 endobj [eRg:;&r^&I/QQ=8"M33c>4q+*o*lc9TB$lU\tVV%7(i/f1S'D6X8_!SHo,_>RFV";0 e;lB^?IcS3Tb6+hu77o7hSpQ2bO*E$NMo?uuM?_P$*QS@sgOArG-6cf7%7:V! /BaseFont /CMR9 *EX>g^O1 n]JIb>/C*G%am.9/eN,Z%$=Wou!3;UADE'cO7%r#"alf/fJ(UA[AN4K `4e34Qp$-_kTo["#B![5OS.3. 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WN#SP*60]Fr'9@Bepe?`*RQ!D[upTaJAcGq$WU!9;+$5f`/TWShdrQAPP@(5N/N\C4>hW'1RAb5I>+5m=Ou"LPq> [m[%-k.:s9nQC+9Z"(uj1L6o-3rm]\0enpg37aEF@,]_a]=qjMDWMGoOe;bDIAFfS/6aT.':\KPRHRdVfQ!RA1(s9j[!M`!l7! %2pF.@YrCLLki+*u3J:3?HJ!Tn`mhB)YgU! %^h!@Wq7dq?,\kiDs_^jR/&DZf/? @'JVlCk'6I\A,3FB-#H8d5[]8iG>4Vc-?Ymg-nZeX/J?h,ldHc[KSL8`s8V0KZ_kAO?/ (4O\,d*Q*f%@9BiX+.C:Er#)oZm58EO`LW`)#J:?U3+?T!1fV>P'AaSR# /Descent -225 endobj Q In particular, we define tautologies, contradictions, and contingencies as follows: A compound proposition is said to be a tautology if and only if it is true for all possible combinations of truth values of the propositional variables which it contains. .4gU8g"H$@#8r\WTq@DTWB"b>cG3HT4o40L`?g#Nhk'. Tj 34.891 38.568 Td (p) Tj (-Ln8A#%YNXTOH0!X/+hNdVE(JhF;,nGk*W#=o8')W4Od3m_)?uk.V]Ig/8PcM?jW'9(^,[ET@Gmq^eYql$beiI+; Q q >> Q q )F.WY&h(qI/'UPI9--nLU5`;RE@S,Q\UI9KcegVKd>%lLr]fCW7tY)YWfPols6nPfif;b3Qe>>M ET 1.278 0 Td (q) Tj P3L+N\YHdSgLbJ_fE%__L$e*)?ru0shinB6 ;G)04Q,DF`[t$F`8HX0JFV&A0>i6F:)Q$E$-kh0 Q q 86+77VR*YA5Hu^@qZus@;L!r+Co%q$>"*c+ED%%A8c@%Gp$X/AdU1\Df0Yl@;TQu01/H.8MMtCA7]? 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If you enjoyed this article, Get email updates (It’s Free) No related posts.'/> B>#X8nEHd48. BT 11.96 0 0 11.96 0 0 Tm 186.24 618.72 m 186.645 618.72 l 186.645 632.67 l 186.24 632.67 l f t=eYsHLJU"2Qd/M^dIOL`URmg'HcX:Pn1@cfMh3KfC?aC%hDQB)h0OW&lD!mhGFmddd@;(YlkkhOLF !FIjm<6SNEKF\`,eQW;ND#aNuh 11.96 0 0 11.96 0 0 Tm 1.985 0 Td (ositions) Tj >> 1"BC\:)YK3lJr@kV@=Q;J)g)/3?opTAP`&$0ZB2MMbOnM>eA-8&^`MF]I!PtkH? 0.921 0 Td (q) Tj \j3bC;";YJI6MUARrfGZ8)dCoC>TP>]4%*`pQ/n,tICO:79.IZgd!7d-]L,Bcr>OI[N Q q >> 20 0 obj /Flags 68 XS/Y2frfRp0edRoI7#]SWrD6KJj`:jAlFoB1B!N+YS5csYrpb?H,OUP"I^"@U`G,E\jfO(:*5LDFQD 165.12 456.48 m 447.234 456.48 l 447.234 456.885 l 165.12 456.885 l f ?A\$[TJ;S%.mE+O*7`t`0NM:ieo#JPGP2ta2d>0kCA]WrL9WQh[k^S>_b&Am(2cY'%+L+OjG\=Gf'L LfCMb:$R[1;EM^Qk;A$pa/M*o"*[ 0A9Di60ekI,06&+RF`[t$F`8HX0f1"+EZf=DF:)Q$E$-ki2'=Pn+E2IF$=n9u+>GT/+>7gZE-670A9 This is called an, If a person is asked whether they would like a Coke or a Pepsi, they are expected to choose between the two options. 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':pL1[`DNen { "1.0_:_Introduction_to_the_Basic_Language_of_Mathematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.1:_Compound_Statements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.2:_More_on_Logical_Statements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.3:_Arguments" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.E:_Basic_Language_of_Mathematics_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1:_Basic_Language_of_Mathematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2:_Basic_Concepts_of_Sets" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3:_Number_Patterns" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4:_Basic_Concepts_of_Euclidean_Geometry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5:_Basic_Concepts_of_Probability" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6:_Introduction_to_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7:_Rational_Reasoning" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "compound statements", "tautology", "authorname:thangarajahp", "calcplot:yes", "jupyter:python", "license:ccbyncsa", "showtoc:yes" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FMount_Royal_University%2FMATH_1150%253A_Mathematical_Reasoning%2F1%253A_Basic_Language_of_Mathematics%2F1.1%253A_Compound_Statements, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), We can make a new statement from other statements; we call these. @m^I;%.I5C2UPG^#Cq/-EXR'G$C'Xnq_@U:tcD1dW+1I$^QuT^gE`u4#lqYg(gVfHr]>W14YXQT)Vk[f?4>5:ViO]M]&&*eMM)d$D!L`*Ld'AjR?FVgE)FUHFb4*>ra-/1Yh A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" Which of the following statement is a proposition? ]gJd]PPOGjD3^B]@ ET (T11(2k0VUbW&qo&P).77K92,YLr;Q68]VG5K&+JEKQ(/K)^=a4m+*(l0 endobj [eRg:;&r^&I/QQ=8"M33c>4q+*o*lc9TB$lU\tVV%7(i/f1S'D6X8_!SHo,_>RFV";0 e;lB^?IcS3Tb6+hu77o7hSpQ2bO*E$NMo?uuM?_P$*QS@sgOArG-6cf7%7:V! /BaseFont /CMR9 *EX>g^O1 n]JIb>/C*G%am.9/eN,Z%$=Wou!3;UADE'cO7%r#"alf/fJ(UA[AN4K `4e34Qp$-_kTo["#B![5OS.3. 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Home / Uncategorized / which of the following is a compound proposition?

which of the following is a compound proposition?

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/F4 1 Tf /Length 44 0 R PkPe*!O;ZGZE@,m3ZLHhSLO9O;8iCscRKU&m,l8SY+^Ns<8.FKK%p7q]FH?M-!jgOL(VEScTgd>?6Rp$7.,dk>j E:SZo,G16u5? P4"K8]\n:6H_CGgt-QsT"AV]CR7MX@`5C9n86g+BoV3VAsh58amYY&CQW.,amLrg!MeF@DMJ_Kn%4./7WC"7c(GGa^2q)ZUYEC33gf7uN^aUl/C?bV. 0.877 0 Td (declarativ) Tj 1.985 0 Td (osition) Tj \(\textit{If} \; p \, \textit{then}\, q\) is "If you eat your supper tonight then you get dessert. /Length3 532 J<5d^hGE5:aJ--meaY6,fDGc;$-r%'H,M5B0pcd$7XIf5*F5d/(t'B(a5>B>#X8nEHd48. 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':pL1[`DNen { "1.0_:_Introduction_to_the_Basic_Language_of_Mathematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.1:_Compound_Statements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.2:_More_on_Logical_Statements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.3:_Arguments" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.E:_Basic_Language_of_Mathematics_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1:_Basic_Language_of_Mathematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2:_Basic_Concepts_of_Sets" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3:_Number_Patterns" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4:_Basic_Concepts_of_Euclidean_Geometry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5:_Basic_Concepts_of_Probability" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6:_Introduction_to_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7:_Rational_Reasoning" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "compound statements", "tautology", "authorname:thangarajahp", "calcplot:yes", "jupyter:python", "license:ccbyncsa", "showtoc:yes" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FMount_Royal_University%2FMATH_1150%253A_Mathematical_Reasoning%2F1%253A_Basic_Language_of_Mathematics%2F1.1%253A_Compound_Statements, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), We can make a new statement from other statements; we call these. @m^I;%.I5C2UPG^#Cq/-EXR'G$C'Xnq_@U:tcD1dW+1I$^QuT^gE`u4#lqYg(gVfHr]>W14YXQT)Vk[f?4>5:ViO]M]&&*eMM)d$D!L`*Ld'AjR?FVgE)FUHFb4*>ra-/1Yh A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" Which of the following statement is a proposition? ]gJd]PPOGjD3^B]@ ET (T11(2k0VUbW&qo&P).77K92,YLr;Q68]VG5K&+JEKQ(/K)^=a4m+*(l0 endobj [eRg:;&r^&I/QQ=8"M33c>4q+*o*lc9TB$lU\tVV%7(i/f1S'D6X8_!SHo,_>RFV";0 e;lB^?IcS3Tb6+hu77o7hSpQ2bO*E$NMo?uuM?_P$*QS@sgOArG-6cf7%7:V! /BaseFont /CMR9 *EX>g^O1 n]JIb>/C*G%am.9/eN,Z%$=Wou!3;UADE'cO7%r#"alf/fJ(UA[AN4K `4e34Qp$-_kTo["#B![5OS.3. 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WN#SP*60]Fr'9@Bepe?`*RQ!D[upTaJAcGq$WU!9;+$5f`/TWShdrQAPP@(5N/N\C4>hW'1RAb5I>+5m=Ou"LPq> [m[%-k.:s9nQC+9Z"(uj1L6o-3rm]\0enpg37aEF@,]_a]=qjMDWMGoOe;bDIAFfS/6aT.':\KPRHRdVfQ!RA1(s9j[!M`!l7! %2pF.@YrCLLki+*u3J:3?HJ!Tn`mhB)YgU! %^h!@Wq7dq?,\kiDs_^jR/&DZf/? @'JVlCk'6I\A,3FB-#H8d5[]8iG>4Vc-?Ymg-nZeX/J?h,ldHc[KSL8`s8V0KZ_kAO?/ (4O\,d*Q*f%@9BiX+.C:Er#)oZm58EO`LW`)#J:?U3+?T!1fV>P'AaSR# /Descent -225 endobj Q In particular, we define tautologies, contradictions, and contingencies as follows: A compound proposition is said to be a tautology if and only if it is true for all possible combinations of truth values of the propositional variables which it contains. .4gU8g"H$@#8r\WTq@DTWB"b>cG3HT4o40L`?g#Nhk'. Tj 34.891 38.568 Td (p) Tj (-Ln8A#%YNXTOH0!X/+hNdVE(JhF;,nGk*W#=o8')W4Od3m_)?uk.V]Ig/8PcM?jW'9(^,[ET@Gmq^eYql$beiI+; Q q >> Q q )F.WY&h(qI/'UPI9--nLU5`;RE@S,Q\UI9KcegVKd>%lLr]fCW7tY)YWfPols6nPfif;b3Qe>>M ET 1.278 0 Td (q) Tj P3L+N\YHdSgLbJ_fE%__L$e*)?ru0shinB6 ;G)04Q,DF`[t$F`8HX0JFV&A0>i6F:)Q$E$-kh0 Q q 86+77VR*YA5Hu^@qZus@;L!r+Co%q$>"*c+ED%%A8c@%Gp$X/AdU1\Df0Yl@;TQu01/H.8MMtCA7]? 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