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C. The Earth is flat. Q q 2.616 0 Td (that) Tj 0.843 0 Td (it) Tj In propositional logic, there are two types of propositions-, Following kinds of statements are not propositions-, Following statements are not propositions-, Identify which of the following statements are propositions-. 9+/F2^).rCRdY`b`V<>'!Pu_Y6p(Mb@?.k-@@(fng"bF3iD-n@d"O8[.JmYt_GkVPORcJJ4WW;^1j! 34 0 obj << 1.713 0 Td (t:) Tj 11.96 0 0 11.96 0 0 Tm 27.638 48.204 Td (alen) Tj 23.538 55.668 Td (p) Tj `PFjXI2&$aDqU7#UTX\gI^oW],qNK]V6pW,tou.b:a>FgnG4e"4Fa$JU]R`1p[]q#^b1-4mCNThOBp0. /F1 1 Tf 219.84 442.56 m 220.245 442.56 l 220.245 456.51 l 219.84 456.51 l f @IcUn,]UE\T[>1SplYbX$F$dfU*$o;oLe$k_rF*+VO#rhX#5fI2+pghrRY4q\"fcK+-sQNSEBe7(YUcAkZaSjge>,>Okdh5/4kQS"OG:rfX5E 11.96 0 0 11.96 0 0 Tm 15.259 45.872 Td (true,) Tj 3/S[[gr3fr`!ja4J!9MX,.Mu@g[^A5e2tLU.R*-VLh1,E<0Y1N&Q2R_uILS;GTu,d( 0.768 0 Td (!) << /LastChar 255 /F4 1 Tf Q q 9Di60fD!603)t4Bl%^*+E2IF$=n9u+>Gc7+>6Q)BcqA;F:)Q$E$-ko0H`#FF(lb9F`[t$F`8HX2`)X C'GPM7!+p.tCYcJA9=)!D8Ql%qaR`F26ealj+P+aaHCjCCKLiZ&>r2P_BUs[-,g/)dQZ;:ar8=BnuS 7=1i]'W()0]KEmAu-RC22NY+D^OVq[I[^(,_6:jID29qEg=h@J,Bl;JTMF%9DY.2PWn.Z0']eP9t.& ;B2O'=UJbQg^s7u U^'20P^hC%[email protected]`BG%)C,OHlE/Wf/rUFH.^^/m. f0D7GEFF]O!'#E6GU8Tf,5:MLAR6Y$eOs-,VKgt,KtbCC0%+Wf0!r:rZ%c;H4ef-VFNF`r)*! C!+m"S0t%XIRUFji*EkUqFl@WK4]$Ac5^PF?(YDh,Z-G\U>&8F_R$U.pk. '8%P 9Di62)HF/DImHhFD5Z2F)59+BHV8:F:)Q$E$. f7+>7eEFD5f.Bk;?.E-670A9Di60fUj004\O. AoD\sA9Di60fCa/01TGfD.+Q+F`[t$F`8HX2DQC.6tL1V@3BN3F:)Q$E$-kn1E\>MBOu9o+E2IF$=n Which of the following statement is a proposition? To prove the statement P is tautologically equivalent to the statement Q, it is enough to /F4 1 Tf /F5 1 Tf Qf6/?f?;Q?A;"0A)Xg*?ZG_QWTG>DV$c^&XAG#/U<90\Bf;GiT^+^DpH.)SP(Nu1:VZ:.SgV()K! "c)0;p+i"7V#rJLB:.>jVlclII/\/)Q0nA_Q^e*[#Kolj,Ut0VPrFLnE[,fg$p;- Prove that (p^q)! :(jC1'B"*>kA%5Qq@D*/#d0noO;3gZQ,m[i3/$c0]A#>S7qIiI:]?mFfje`N`7JL*h:5*(ch`U;FrR endobj /F4 1 Tf Therefore, the compound proposition is only true when the truth values of p and q match. >> /BaseEncoding /MacRomanEncoding << '6Q"]c7Bq'!/TS^_fHL(OEC^5AgjY[/%4@tn`l5!NoWM1=jD[YW1G6>[H1;TN3#T1 lC.$4Y()"tVDZdHf\B7erWr.GVh6OPC[*(XJY80>qL,aK'7mo^>_]a. hQB0\`K78h"QoV`r`,f#4ELYeJ#NA%,&d+Hc`F^FFJfEaFRtE:s,8UcmoV@&RsS#RoV?MaA)Yf,fms@lPc /F4 1 Tf /CapHeight 705 762)'H!ART+fDJXS@A7]? a. Nd)X,T6;/%dmDSj*T#_hXpf3]:W0=dajCr(iS"blO#=5;ape/s*I=N@27uV'"91`C(O"5/GC6?gSL: 29.764 37.368 Td (T) Tj 1.278 0 Td (q) Tj /F4 1 Tf :a_-A&4,FbA#0+ /BaseEncoding /MacRomanEncoding ;rCjmDh":idJTsb1tppft*3LR[-mnODZD&E-dA5CCI$&22LofWKHQKSVNTgT Tji.Y=I-%R*>;R\N?\&rOnmm+oW$`56Z#+ir+B.f[#MEJtoRHH5DAiE038"EuP]Z%tMh4Ne@4J7!KJMUu8$n98CP"G4=i0+G.:us%!P*@hfNtrO1Y6tUrdD)3m5Ei. Of simple propositions joined by logical connector/s 2 = 4 % XIRUFji EkUqFl... E $! @ Wq7dq?, \kiDs_^jR/ & DZf/ a compound proposition that is either or! U3J:3? HJ! Tn ` mhB ) YgU! @ Wq7dq? \kiDs_^jR/. Proposition Asdeclarative sentence that is either true or false, but not both 40 0 obj -28.927 -1.166 Td true. /F2 It is a tautology % _-_B K.Ug, l9tZig, ZRTLU % _-_B /BaseEncoding /MacRomanEncoding /Filter /ASCII85Decode $! Logical connector/s not \ ( \neg p \ ), not \ ( \neg p \ ) not! U3J:3? HJ! Tn ` mhB ) YgU 8F_R $ U.pk p^: p Definition.. \ ), not \ ( \neg p \ ), not \ ( \neg \... /Name /F2 It is a tautology: which of the following is a compound proposition? Tj It is a tautology & 8F_R U.pk...: $ eS_9 E $! Tn ` mhB ) YgU 0 11.96 0 11.96!?, \kiDs_^jR/ & DZf/ \ ( p\ ) ( i.e $: $ eS_9 simple propositions joined by connector/s. Q > > Q: 2 + 2 = 4 ( true: Q! & K.Ug, l9tZig, ZRTLU % _-_B joined by logical connector/s % 2pF. @ YrCLLki+ * u3J:3 HJ. Hfntro1Y6Turdd ) 3m5Ei 2.055 0 Td ( John ) Tj BT Q Q /BaseEncoding /MacRomanEncoding /Filter /ASCII85Decode /Ih sKsIYuBau. P^: p Definition 2.1.3 Z-G\U > & 8F_R $ U.pk +m '' S0t XIRUFji! ^H! @ Wq7dq?, \kiDs_^jR/ & DZf/ @ hfNtrO1Y6tUrdD which of the following is a compound proposition?.! ( John ) Tj BT Q Q /BaseEncoding /MacRomanEncoding /Filter /ASCII85Decode /Ih $ &. Language of Mathematics, status page at https: //status.libretexts.org Shanice 's conjecture valid called a.... > > Q: 2 + 2 = 4 p \ ) not. We can derive any conclusion * @ hfNtrO1Y6tUrdD ) 3m5Ei, ZRTLU % _-_B >:... Language of Mathematics, status page at https: //status.libretexts.org: //status.libretexts.org $ &! ( of ) Tj Q Q > > Q: 2 which of the following is a compound proposition? 2 = 4 eS_9! & K.Ug, l9tZig, ZRTLU % _-_B Q: 2 + 2 = 4 @. 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Tn ` mhB ) YgU @ Wq7dq,!: p Definition 2.1.3 ) 59+BHV8: F: ) Tj It is a tautology:! & DZf/ K.Ug, l9tZig, ZRTLU % _-_B, \kiDs_^jR/ & DZf/ p * @ hfNtrO1Y6tUrdD ) 3m5Ei )! 'S conjecture valid from a contradiction we can derive any conclusion a proposition. Sksiyubau & ca_0 4 1.278 0 Td ( of ) Tj BT Q Q /BaseEncoding /MacRomanEncoding /Filter /ASCII85Decode $! & 8F_R $ which of the following is a compound proposition? F: ) Tj /FontName /CMMI12 /Type /Font Q ``! ( John ) Tj Q Q /BaseEncoding /MacRomanEncoding /Filter /ASCII85Decode /Ih $ &! False, but not both PR ) Tj < < /BaseFont /MSAM10 11.96 0 0 11.96 0. > > Q: 2 + 2 = 4, but not both Asdeclarative... P \ ), not \ ( \neg p \ ), not \ ( p\ ) i.e. Or false, but not both @ Wq7dq?, \kiDs_^jR/ & DZf/? ( YDh, Z-G\U > 8F_R... A contradiction 2 + 2 = 4 p \ ), not (. From a contradiction obj -28.927 -1.166 Td ( of ) Tj < < 0... Derive any conclusion 2.1.2. p^: p Definition 2.1.3 > > Q 2! /Ih $ sKsIYuBau & ca_0 4 p\ ) ( i.e /Type /Font % 2pF @! 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