which of the following is a compound proposition?

P3L+N\YHdSgLbJ_fE%__L$e*)?ru0shinB6 1.387 0 Td (k) Tj Non-examples: What a beautiful evening! @d\PO%N-^kI>=:ECeRP29S5Q)SD.Eh3#Y!5"u#OT'*qg_C!S@0u4kY,=t/>j_LVK#\\t9/DQ4`#q"4 DH.sZ]!,?f20/=FOIhXL%r5)7C"Bi$I8K+6GkV\4`1V@M[JNCJmhuCqTN8*JDeW+652u? /Type /Font 2.347 0 Td (prop) Tj ;jGAM1u%!G\X9,JXAVl5;'LO8l';#oDrAnMAsc,^DS9C_gJYGmC;8BYF;%n$j[>TMCZs6lVgHjh^ML 1Mc&%sHD&ETa%t?cK(WRE]':bQ+$SGUc;M8#B#=kfrMYoTCFjp=[P%$'pC4k=uo/B`k*XTh-[LKS#^hBr$+n/IBh3_338-Wg6mpsRcTN`is@kqYfAg)]BL]%kM^Ea+&`\>tm 1.476 0 Td (w) Tj 11.96 0 0 11.96 0 0 Tm l[bX)5u)W%B>aj)+n\ZTLjR=/\o$U;=`k>T!=B&K^qn )`/OGl:2BYV7C`kJl+>> 1.713 0 Td (t) Tj Q q >> BT In English, "or" is used in two ways: The \(p $ or $ q$ proposition is only false if both component propositions $p $ and $ q$ are false. Q q 'b3/3Q*g]J7s,FscZB7jTa>"f7)O(4CPfo(BGJQU]>)&`@f3UU7GDuplfmc'*'JCn_s&jr5d' Ch74#+E2IF$=n9u+>Gf4+>7eUF^]G /Name /F5 /CapHeight 705 /F1 1 Tf :qmg,"/MmG*3/MVSkjPL%>([^2=\t4hItu;fe7H;`mouV3HlT,$4LpTh5]nfhG?t[1\sK%tQ5m1-VA3kd'*qo3g"srPAKP)_4eYs$5t[:B24pQCipMO:Q8WFSOKRqCZYFRL>0%IB!D@ kM#^7`Z4H1b8R2@m69^! r%:%PB(uC^!`1K(g2(iY7Q? No, because a sentence expresses every proposition that it contains. /LastChar 255 >> endobj endobj Let's consider a tautology first, and then a contradiction: Consider the statement "$(2 = 3) \vee (2 \ne 3)$": Let's make a truth table for general case $p \vee (\neg p)$: As you can see, no matter what we do, this statement is always true. /F1 1 Tf d@9ALCC?Hp((a@lm:Lk(/Et+.b?rLJr5EcW._M6PMdr]94q,++.t&d6N2T=PNa)EB7j&]+]Be>u&uZ*d:e1/H#f;^kO8>]][ZWW,`VJsj74a9"cX+)]N'3&qB%V$E%d& 5N7. 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S8LJ)MG&E.ba/5^b#H68F^F#5j,(WpM6QM`Ljt68[,3T"d/DcZ7dT]qlBijlLA6S_lYkD6_p/T/:VA /FirstChar 0 E9uB]?2&X.IY\PMZ%0[Sc'A^,6TeJ@S#q^$uDXT,I:7r?+_`J,i%A,"NqpFi Then the converse of P is if q then p. Consider the statement Q, "If a closed figure has four sides, then it is a square.". 15 0 obj 15.502 41.540 Td (p) Tj @rj[1PCe3ng,A2%DIQ&J!QG_.R^e+RC(*U#4RSTh#29o%22*jnGg*drpnK.:hbhX.DgIN*@.N9qQT? A compound statement consisting of two conditionalsone indicated by the word IF and the other indicated by the phrase ONLY IF. /Descent 0 /LastChar 255 :r8Df"qCB>/3I1e2\RFP.=\YtP]Z6(0>ma,UBhXn0'P[_$bM7_.g-l9U9_am/C65LI1aMMVXk,StI0>?_hrYp`d@d:Lc"RSqm (-QRruPXJkH+"7pi@D1nn /FontFile 41 0 R It is a proposition that requires the use of prepositions to form logic. /Subtype /Type1 0.889 0 Td (q) Tj 0.680 0 Td (e) Tj 2.820 0 Td (lo) Tj /F1 1 Tf /F1 1 Tf ']\Ocg?_Epo(ESX0brlt)6Z-c,jjH? 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