which of the following is a compound proposition?

NEeN0%gMu-+d.0DuP`Srp!5$p]]:VkqOEU'>6l#X0hY7';).qT1[8iIoJ5=X9f0`JeZe`XrFil##d& /Length2 10935 [SKR=2In#i The truth value of a compound proposition depends . m3V3>EW2+g(X#[Z=]t%D:SDZ*8j,>!>;KcMt^p=,p=4LtNi#$jpD>;agWNa4;N(a/g4>N%lqKrIB.O .>ET+1/-;cL8&E@ZihJOk7\=S6Zu4bdi*GQr,SnH,L;_6h_@1lCXY!+Ou$=QV'=s]Z8EOZ`UW=S><6p]ZRcu:U?6,sY+,,0(kM*8@e,P/#ApUh_$>OlN(Hpja\R j%)Kdp^tjGWs2=o/(`a`8(]]sKMBd'nLT/ETM.mOA3m4+H110O/n>@nm:oRZE8>bke`]8WuU=?e0L+ /Length 53 0 R /FontDescriptor 24 0 R endobj &/0TX7&I`39%7"E@p_kXLK3MsYb:c);5U]=5c>5(9tc/mN? 0JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170FBKf0JG170JG170JG170JG *&"@:X:oCj@.6AS)9&7W30d6:,U8HS%!5+>#T30H`))0fC.52`6#(ART+fDJXS@A7]? ]#`<>&caeAS+4N4YkB8F&ChWj=a;i,L`=-=?HbQ]3r"lTGk[DUM+Z1bq^a^/&. 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This is, is (p q) r logically equivalent to p (q r)? /F1 1 Tf *\UE[m1X?ZsYeN+,eu#iLQFUtRB;`]";jcKLN#n1na3h].NCR'?6jc;'q:1PF'"^o8q"8suGf-Nko( /ItalicAngle -14 ET `4e34Qp$-_kTo["#B![5OS.3. mt+BS$j`;2)iX`PW!b6Ua"fjG:)c8[(^+=4)8r!52ePpZ5l8V2A1&?YDfqiO;f%Yi/uZjliBtF(9$] IJMs;=b70MVc&?;B.?PFPQ=o[?Xne:-?&8O.rdA/eK\Y4>. BT ,p?)`/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"FdART+fDJXS@A7]? ET /F1 1 Tf Q q "EW4CA(IqpG\YA43^,GuF@-MH(Bm3M 1k%_//(6[lc)gDdW&jM&lpn;#7UjTr_VIg)N&9n#tc647+/FU7:cXWn3Ih71eq;dYf 14 0 obj /Length 52 0 R [rOT\N*Im&lYSbn?5OmtHO_Bj$h.gT9@='LhZ)tj[N2`aX%7qNV*.JW30>C+8 /Type /Font Tautology: A statement that is always true, and a truth table yields only true results. 0@9pR?OA>>OXTX@E.e]XutcXJpiV4/O0pZmV1G.pe)P9(6U7^Mh(;l@j*3ErogA4E!_e.uj`(S7p[F @C9? 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Please mail your requirement at [emailprotected] Duration: 1 week to 2 week. V/F+2T(5V3a`'?%c4(! /F5 1 Tf 33.579 53.269 Td (F) Tj 9Di62)HF/DImHhFD5Z2F)59+BHV8:F:)Q$E$. These compound statements are true if both component propositions are true or both are false: Consider the statement: "Two lines are perpendicular if and only if they intersect to form a right angle.". aU$BPmEW_VKh@m&*1W#YB2S7h(nZgMjX! /F1 1 Tf rfI*)sCl)A3Xs32.jQ*sJA2Ae/%ir?cY&=r[;-L/$>MRKI#l/LW^25]@8!rAp_9SidYjG5Uc]%Gcf! MM7jpA:*,?bai[84\]APZSAY4*^]BKPR3B/a)h)!M+^3q^)e]Ha3sM.IX_Nu2,Fru0jU=+M/m!,^,5nqa.up6bf,cl g]q(Z"T,/%.MIC)J,,b&k/?=^"lom50f-dNXdY[_?1Cs;cML9)?=YGBfJ6=F:_HDT(tKf&IU"cjl6> kTJK-D*P5e"#!Rh)@!i'(?e7J+G'c;ElF,%VdPj=pUu>8=^@AgQ0"9"?&S%;c&IQagglqWUlL#Qs$OAqr"cHL9Zp8?MWR#EM;F-SKO-D50=]k+Hc`N@foB3JY;5TD7oL-Vs Q q ET BeMf*bEo;S!ph2UJ0=oC6->NF%47)MPI0U1B"lD;I7DiUFSO'I0rp`^b,8h%`hGS-f 0.381 0 Td (p) Tj 2.339 0 Td (sen) Tj 11.96 0 0 11.96 0 0 Tm ;>;ktDqrS(a ;;`Gi1V)8X]Mg@F(rgNmZOL=$eA_7!W]/a&I-YY&-Zu(("u`R,6W1t4H. 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Here, All these statements are propositions. /F1 1 Tf 23 0 obj 11.96 0 0 11.96 0 0 Tm %^h!@Wq7dq?,\kiDs_^jR/&DZf/? Propositions Examples- The examples of propositions are- 7 + 4 = 10 Apples are black. t$7er7o&5-I:P37DiXp`R+.? Bp/HLJ(B#`! True. 201.6 456.96 m 202.005 456.96 l 202.005 470.91 l 201.6 470.91 l f &6MBS:`O$.buj/lg9\DfW7LDp#86CI*[b55X+EZ@TY7@XDua7($l.74rAdT"#**2amh-C4W[t]I&pg Q q Q q *\UE[m1X?ZsYeN+,eu#iLQFUtRB;`]";jcKLN#n1na3h].NCR'?6jc;'q:1PF'"^o8q"8suGf-Nko( 28.103 16.119 Td (q) Tj d@9ALCC?Hp((a@lm:Lk(/Et+.b?rLJr5EcW._M6PMdr]94q,++.t&d6N2T=PNa)EB7j&]+]Be>u&uZ*d:e1/H#f;^kO8>]][ZWW,`VJsj74a9"cX+)]N'3&qB%V$E%d& 1feA! 9_Gg$P3u'bhSU;p&FjLfraZ]KX1J!r)nri'lY\;5?O5W*C-LM00JT /F4 1 Tf BT 5Oo>?bT@j&>,^bKSrs'brD4+TW1@#2)6']KJ^;SL\3.%R*V_p$sW26ggK1Ak%"9s*jO\asS#Z=#.33g+69R(Z6JI ]gJd]PPOGjD3^B]@ F0dg.%#o'8jW*HZ,s#C:U/cPdem!_U\J"XY)+hPj)EC_RJsD%-lb0H_f\gsM0 33.545 54.468 Td (T) Tj If x is an integer, then x 2 is a +ve integer. >> Q q >> Q q %^h!@Wq7dq?,\kiDs_^jR/&DZf/? 1.985 0 Td (ositions:) Tj 26.859 33.770 Td (T) Tj kIo^(-L])h8o1[+6`nU,HF^M,)?dh[OX^,I6qtOH%qu\F?3XV4o%i4V^u1ZJV11=YS,['`GHtB(/QW This is why, if both propositions in a biconditional statement are false, the statement itself is true! BT /Type /FontDescriptor 1.609 0 Td (conjunction) Tj /StemH 20 11.96 0 0 11.96 0 0 Tm [n[LYLKP&asnWkIoG,gOA endstream 2MnP-U4&$G/lYd]1<69D&Hn@TM]aBRZ;8I!`/n=^.h46X;L`U*>7/Wks5mKCWo8:Z:KPZC>CYnm [f BT This can be checked 2with a truth table: The fact that all entries in the last column are true tells us that this expression is a tautology. 1.759 0 Td (are) Tj /F1 1 Tf BT TLE/9[d"mS._5t:8asu[CklKl'1. )2"g\MR[=RE7RQS$+dI![E^-m?%C]9&\B`;*ck`UkGr03j@Zofa/M#YN%#WK5m/%9l6bh.%p?UV'!IC0eakW.R\g]Q+K*. 1.686 0 Td (\\) Tj )2"g\MR[=RE7RQS$+dI![E^-m?%C]9&\B`;*ck`UkGr03j@Zofa/M#YN%#WK5m/%9l6bh.%p?UV'!IC0eakW.R\g]Q+K*. ^MBDOGn8pq;%S4.3oE!VZPI0I[)AaAA]gpo.I:obHnXROdVq\0EK7ZC$d`4TCPu2tBH Q q >> 'o'%\i5-;9KjbUVro_V9a(4e9MR_^Wc0%FSKs+:((Q6`:i^b;\Y/N)=/6rmXk^3&fJ6cJ\ /FontName /CMR9 11.96 0 0 11.96 0 0 Tm 37.923 41.607 Td (\\P) Tj .>ET+1/-;cL8&E@ZihJOk7\=S6Zu4bdi*GQr,SnH,L;_6h_@1lCXY!+Ou$=QV'=s]Z8EOZ`UW=S><6p]ZRcu:U?6,sY+,,0(kM*8@e,P/#ApUh_$>OlN(Hpja\R << ]C4cI1I1Kq'i7o9FF3Z2h2kOBKdEWi<4p!4Q=;VspMsWR)aZ /F3 1 Tf =4NObA3:H\"]bj7AYE95^@+h:fpg,3]]aI2lWtj5? 35 0 obj (I^#h/a,u"rKqgF0aL4k/k3h*hepN5fHpWYBR80&F0g1#adpo4Dj15#.VB& 11.96 0 0 11.96 0 0 Tm Nd)X,T6;/%dmDSj*T#_hXpf3]:W0=dajCr(iS"blO#=5;ape/s*I=N@27uV'"91`C(O"5/GC6?gSL: All rights reserved. /Contents 7 0 R a) Either you leave or I do. /Length1 1754 342.72 399.84 m 343.125 399.84 l 343.125 413.79 l 342.72 413.79 l f 11.96 0 0 11.96 0 0 Tm 20.397 40.374 Td (from) Tj Q q Q q /Length2 18039 >> ."[X3\JNuB_jK0j%!Z4cpKo,R*KE1Mn\!?Pt^$-s3(jQrED!V;2^e+1lP/.=. ;RgBK"Efgb[X/H;ci]nj=p4b1R](@KHto6PdVMr98Q&&IQrkEpn:0DjY#c^$cmF1q[nP#,r4R, KR3=7&T6Z6phEbT0"F^/he^sEb/ZiDf0B:+Co%q$85.mFD55r+=KTqE-ZJ=ol+>>E%0JO\(+>@(DEb/ZiDf0B:+C /StemV 20 'E^aNd6Tj)h)0qJ!hK/$o$YHV"*'Z\MGmH^p#$83/`=kaau$aYl[=sgf*ldl=J-"[rFUqJWq$9T^WF?/1L?L Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Q q << C!S'[A^?k1)'Q&Iud&lPe#,([:Tb"[t8doe`7g)0eW8B4oV7o@-XA$qGWPG\X1"0f^QX6.,OE<2p7D /F1 1 Tf Let p denote the statement: Gopal is tall, q: Gopal is handsome. Get access to all 9 pages and additional benefits: Course Hero is not sponsored or endorsed by any college or university. /F4 1 Tf [eN8,.B>\La"KR68f[/J^@V3E1RN;_:_s,8$0cH_Me9Q@GN%0*2MSp+ 342.72 456.96 m 343.125 456.96 l 343.125 470.91 l 342.72 470.91 l f ZpMd>F_>-'(V5]a#n,\?Y@JjYQVBG@(pLLA`T:$I"amn(\RjEMF')& Yi=g[V:f2*Q)ms,mJsL_L/Hu8=,Ga/#57c\ZbUr2-7TV6=HAV/R^rSFR4qTg!6"u!p3+9R!Uact$+i Consider the statement "If \(2 = 3\), then \(5 = 2\)". 385.44 647.04 m 385.845 647.04 l 385.845 660.99 l 385.44 660.99 l f -25.257 -1.166 Td (prop) Tj Proposition is a declarative statement declaring some fact. 2.406 0 Td (is) Tj /FontBBox [ -36 -251 1103 750 ] %CmT@.Fo"AgLNfr<2eUsp;-kRto!_?]fAc`DELE@3"Um,d,! Mathematics is interesting is neither true nor false. 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Consider the statement "If a closed figure has four sides, then it is a square." /CapHeight 705 1.738 0 Td (ap) Tj 12.091 17.704 Td (Exer) Tj 22 0 obj 1.277 0 Td (p) Tj ':pL1[`DNen /Length1 2140 mW^S"S;#WPqO$6`F=1rDU^X/A@#"0C9j_)E0D /Length1 1754 WF8$#XJ@n[l719BnC^A^Zf?--R_!.QI(,-=k_S$=/mS1h$XMcG4L:1&G50b)$/et4RJcN%OlF>NR=^ Q q /Length1 1517 ET 1.903 0 Td (c) Tj ET (e) Noue of the above: DetemHine whether Or' HOt thie following specifications are consistent. >> << /F1 1 Tf 0.847 0 Td (F) Tj 1.074 0 Td (ws) Tj 434.88 249.6 m 435.285 249.6 l 435.285 263.55 l 434.88 263.55 l f Di60ekU006JCVF`[t$F`8HX0fU:/Fs(aHF:)Q$E$-ki3?Tu!+E2IF$=n9u+>GW*+>7s^E-670A9Di6 endobj E9uB]?2&X.IY\PMZ%0[Sc'A^,6TeJ@S#q^$uDXT,I:7r?+_`J,i%A,"NqpFi 316.8 544.32 m 322.677 544.32 l 322.677 544.806 l 316.8 544.806 l f 1.003 0 Td (true) Tj & 5-I: P37DiXp ` R+. & ChWj=a ; i, L ` =-=? HbQ 3r... Propositions Examples- the examples of propositions are- 7 + 4 = 10 Apples are black Wq7dq?, \kiDs_^jR/ DZf/! 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