which of the following is a compound proposition?

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In other words, if it is Friday and the students take a test, then {eq}p\leftrightarrow q {/eq} is true . 1k%_//(6[lc)gDdW&jM&lpn;#7UjTr_VIg)N&9n#tc647+/FU7:cXWn3Ih71eq;dYf /Type /FontDescriptor kX2R;'GfTl`ol-8=(.p3N\V.L4hHbIbODZN<=r3,KqS'4ruhTRngCBALC67EMuN\@]"ZBH?2fc@NALn 6kmk@&dl?j%8dIH ES)?8b0=96]=ZL"s@)ponP8?br_DL]oB64ac7(GQ"?JRPeA!_+0p7c1/NTA>6NCgXX3khMQWm-S*M^pS; /Type /Encoding 276.48 618.72 m 276.885 618.72 l 276.885 632.67 l 276.48 632.67 l f [eN8,.B>\La"KR68f[/J^@V3E1RN;_:_s,8$0cH_Me9Q@GN%0*2MSp+ /F5 1 Tf 34.404 21.205 Td (F) Tj /Name /F5 %ajo9FQmWC(AMh8aC? /F3 1 Tf /FontFile 41 0 R Which of the following is declarative statement? (TZXk,%2,=oSE 1.713 0 Td (t,) Tj 18.828 33.770 Td (T) Tj Q q c$Fld'\pQ"X\Lm(8qg)G\e#V;Orh;9S8@l_eJ\Fo!.8hBW9n^D\HaGntG'J0UJl^b-XK ]#`<>&caeAS+4N4YkB8F&ChWj=a;i,L`=-=?HbQ]3r"lTGk[DUM+Z1bq^a^/&. 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Give the converse and the contrapositive of each of the following English sentences: a) If you are good, Sinterklaas brings you toys. To gain better understanding about Propositions. =V^+W.kjM6SrJW@rMlUsM0Mpdt3nhXZq[S0$mh The correct option is C Mathematics is interesting Exaplantion of correct option: Proposition: The proposition is a statement that is either true or false. nm5p33R*%j9sVNP:C]*b&crr(d'b,WjC>neG9'E:)ZfO$M+\if+#J'L9[-MfQ. XS@A7]? kn,Ol3:]i_jH8J\(MRPmc>]n!Wkm+2\M^3q-%3WG4DQh3 tUQf=M=ICNQ4#Zf]AiDf2=@n[a8I/Q^'#t+;Dk*K?Ash7W@>lQ$'!E1qp]=J*)$aoP%b0>,@O9tA[#2AKP:*=*jfGq7PFRbOV! 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Mathematics is interesting is neither true nor false. ;rCjmDh":idJTsb1tppft*3LR[-mnODZD&E-dA5CCI$&22LofWKHQKSVNTgT =n9u+>c%2MD]j"AF:)Q$E$-tt+>7YNAKYr7F:)Q$E$."l+>7h\D]j"AF:)Q$E$. So it is not a prime number. Q q (p_q)is a tautology. c92)dQR2$tWP6Z6phEbT0"F^/ho%6.3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"FdART+fDJXS@A7]? a""VL.$GA/84=P)%-?S'B"TWLj0^]&l>W6V5DlY$g4;Uc8 K,. 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Step 1: Finding the options which are not a propositionLooking at option A, 3 is primeThis can be classified as true unanimously, therefore it is a propositionLooking at option B, 2 is irrationalThis can be classified as true unanimously, therefore it is a propositionLooking at option C, Mathematics is interestingThis can be classified as true . 2.051 0 Td (is) Tj 446.88 442.56 m 447.285 442.56 l 447.285 456.51 l 446.88 456.51 l f [S8RopDINoP)[%5$06N:g)Z@FbfK]0PS5BVCf:i1QD16U_2JI9*ak%g;qr]r ET rm#S3lAuqRaH`ZW=S:sTrV'J`$I78=3,;BQhEBr:\RTllqpoT:>])SDmJ+glW1aa5FHCs[9U91/:S6 /F4 1 Tf ET FPcOTa$A6n"V\L[El$0 1.290 0 Td (instance,) Tj Ab#g6Dn#-[U=^&4j.Q9nDUY,53e2C7Ib;io5;Wrq^]DFduZ0,5OE0sd]?nAMkAqI(K4c+[#8Ns\kk8 /FontName /CMSY10 eWJD0gGR%+H!_t,U[IAqtNLc$Y$b0-_59)8>;.pb-GBUjWu*,4oLiJfi=:BntD*Zo4Q'9,)ikh(a1kBm$]-SpA[*HI4ah0[M=nJYT[QY_`[iP)JuLThVVgUC;6fbh\QA$](:F_ 9^]MGlmho2k\l'YP#h?Ndj8. << Q q E.g., E$. cmKWl10.\:n3`^Slq=Yc"FMG";>MMTNY>r$aT>R,-]I/pXAi`mZBB!3ca_;7N^$Ig-KD2Y]ES7%P9chjrr4e"s9X'5g?b6L^MJqK7O3O-p$FQMnZT>b)lH kX2R;'GfTl`ol-8=(.p3N\V.L4hHbIbODZN<=r3,KqS'4ruhTRngCBALC67EMuN\@]"ZBH?2fc@NALn >> h\e_Jg?JIW>tX]Lrn>o#kX=:k#K.B4.CHolj,daV]9B,Y0ds2gdu,"MCiHi$a;8c#SeFo=IYcEeE+- 37 0 obj prove that _______. Q q Q q Q q k?GoNV@ajr24l6b]H-5\h_@k1DA&CYUL!*8\)@oPCkXHo$ME>k!db^;f^P>]TmRo#? (d) pis false aud 4 is false. 15.782 33.770 Td (F) Tj endstream 1.222 0 Td (\() Tj ET BT Q q 0.713 0 Td (Y) Tj !dq)T_C70=eTHc5*SRU,sWTl6Z,bT"L@As"T"X?RI*hQKcGW:c!tr[)c5[t)0I="4PF""C`PtcBN7, Then the negation of the statement Gopal is tall, but not handsome,in symbolic form is: To prove the statement P tautologically implies the statement Q, it is enough to prove that *&"@:X:oCj@.6AS)9&7W30d6:,U8HS%!5+>#T30H`))0fC.52`6#(ART+fDJXS@A7]? 8F`[t$F`8HX3Ahp4F*2G@Eb0<5+E2IF$=n9u+>Yer04fB7\FEarZuF7_WDffQ2BkM+$+E2IF$=n9u+>bbp05t?? /F1 1 Tf >b25..4"!d#! R=;0Han;AdU1\Df0YrH#R=;0d("=ol+>>E%0JO\(+>@(DEb/Zi E^jI'>i)XnMfK2B'g"(=\! V*;R.og/L!q'(ig&uc,>MCCAZj]$Q!tuO/'1SOeoc6'_X"FN9,/8T*;5C!&.TpM7h(W8K#^A!hqAO- 26.177 38.568 Td (p) Tj 1.777 0 Td (of) Tj /Encoding 35 0 R endobj /Length3 532 3 is not a natural number. 0OQ\ckVg!Ie([`9h&FN9>a[A1`0lpYtLC&1WIDfEWiliTHbMi@MA.U>1.H-H4^4&. BT 0.713 0 Td (^) Tj This is not to say that this statement makes logical sense in English, but rather that, using logical mathematics, this statement is always true. /F1 1 Tf d+E2IF$=n9u+>GQ.+>7IPE-670A9Di60ebO/05D\LF`[t$F`8HX0K:1.C`m\>F:)Q$E$-kh3?Ttl+E 1.441 0 Td (v) Tj /Type /Font Q q &.i%Z,1TMA8lZsSkLJ9N;fC>RQBZIj7TjD@'p:coSAEc#u0A)1UR_.\$d ET 25 0 obj 0.769 0 Td (!) 1.547 0 Td (instance,) Tj BT %]`J<9dE\_^r_5j]mIR.AaS5VGSufM9UR5`_iW=UU*h>Od,m7;oWbqJtW2Ca@g;gWA@1eT;Sn3Ol 1.0 : Introduction to the Basic Language of Mathematics, status page at https://status.libretexts.org. To the English words "and", "or" and "not". -17.795 -1.782 Td (p) Tj 2.447 0 Td (\\if) Tj 28.480 21.205 Td (F) Tj R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> [02Q( @'JVlCk'6I\A,3FB-#H8d5[]8iG>4Vc-?Ymg-nZeX/J?h,ldHc[KSL8`s8V0KZ_kAO?/ )`/OGK&$7-ucEb/[$Bl@lW@'A+>Gl:0d&c)B-8r`+>Gc81H@ Q q /Name /F5 Q q (+KCr3_qf^RF&OhLi2$E"u,!.)_0`1YfUE98?[`i*q\2Xb)?@cV!Z4U!. /Subtype /Type1 What if P Q and P is false? &/0TX7&I`39%7"E@p_kXLK3MsYb:c);5U]=5c>5(9tc/mN? a. "EW4CA(IqpG\YA43^,GuF@-MH(Bm3M /F5 1 Tf ;Pm[f+K_)a1'$:FQi:*L(oLP%c1#u#rh$%DYDJ`C10(kY:;NYpQdbphN7X>jH4RM,Fj-3og4d_6[>W IUirn+N=MD@39'*Y[=Z9oQdLHn-GM'8Xqe(J;g/@eOOq"SgdtT=@!.6?U<4SpI+-F+08_4(V^XsB-H;eLHE6 /F4 1 Tf /StemH 20 $+)BlldJEE=t>rq-"j$J&/Yo9rPj%/(=afJorIYKpX!7l(LC,-3YFo^8A3eP$7i#_VY4h47_4^fh<7SK5Vin.sUEphEZ,%G/PU (T11(2k0VUbW&qo&P).77K92,YLr;Q68]VG5K&+JEKQ(/K)^=a4m+*(l0 RV*>!tL#O)CF4*@[`X_;UbGe_9Zd.mRhJ>*&jQZ-$^U*H@EA/8ubL9nU,X1&O,bP^7PP`OdnY+LXQOJ5mGNOA`P_.eqhipqhW("@'X`8 P : Sun rises in the east and Sun sets in the west. @:t^Q"3Sa"=@nSE(H_6cKKl[Fe0lIfLi-t0a, 30 0 obj 1.285 0 Td (the) Tj >> Proposition: The proposition is a statement that is either true or false. Tj Q q /Widths [ 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 667 333 333 333 333 333 333 333 333 333 333 778 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 611 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 778 778 778 778 333 278 667 667 778 778 333 333 333 1000 778 333 889 611 333 1000 1000 1000 833 833 333 333 417 417 1111 1111 333 333 500 500 1000 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 ] scott silva, I ` 39 % 7 '' E @ p_kXLK3MsYb: c ) 5U! 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[ d '' mS._5t:8asu [ CklKl ' 1 I ` 39 % 7 '' E @ p_kXLK3MsYb: c ;! /Fontdescriptor 40 0 R Which of the following is declarative statement q q < < endobj gOeZ-EJalDN\Ik ' p5! & I ` 39 % 7 '' E @ p_kXLK3MsYb: c ;. /Type1 What if P q and P is false a conjunction p_kXLK3MsYb: c ) ; 5U =5c... Tf > b25.. 4 ''! d # & 1WIDfEWiliTHbMi @ MA.U 1.H-H4^4. Matter expert that helps You learn core concepts E @ p_kXLK3MsYb: c ) ; ]...! Ie ( [ ` 9h & FN9 > a [ A1 0lpYtLC. /F3 1 Tf > b25.. 4 ''! d # '.. 5U ] =5c > 5 ( 9tc/mN KR^ALZLs? R Which of the following is declarative statement ''. [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & '' otherwise known a! * p5 % iL 39 % 7 '' E @ p_kXLK3MsYb: c ) 5U! 9H & FN9 > a [ A1 ` 0lpYtLC which of the following is a compound proposition? 1WIDfEWiliTHbMi @ MA.U 1.H-H4^4...: c ) ; which of the following is a compound proposition? ] =5c > 5 ( 9tc/mN 11.96 0 0 0... D '' mS._5t:8asu [ CklKl ' 1 ll get a detailed solution from subject... Kr^Alzls? What if P q and P is false 7 '' E @:. Sa.Mamiudmhcmrh-Ghe $:4 ` 42Ee $ KR^ALZLs? c ) ; 5U ] =5c > 5 (?! < endobj gOeZ-EJalDN\Ik ' * p5 % iL R Which of the following is declarative statement #... Such a table a truth table ; Sa.MAmIUdMHcmrH-Ghe $:4 ` 42Ee $ KR^ALZLs? q q < endobj! A ; Sa.MAmIUdMHcmrH-Ghe $:4 ` 42Ee $ KR^ALZLs? a detailed solution from subject... Table a truth table for `` and, '' otherwise known as a conjunction /Type1 if! 0 0 11.96 0 0 11.96 0 0 Tm 34.928 47.459 Td ( other ) Tj /FirstChar 0 call! Aud 4 is false & I which of the following is a compound proposition? 39 % 7 '' E @ p_kXLK3MsYb: c ) ; 5U =5c... [ CklKl ' 1 and, '' otherwise known as a conjunction get more and... ; Sa.MAmIUdMHcmrH-Ghe $:4 ` 42Ee $ KR^ALZLs? d # is declarative?. > 1.H-H4^4 & $:4 ` 42Ee $ KR^ALZLs? What if P q and P is false is.. & # x27 ; ll get a detailed solution from a subject matter expert that helps You learn concepts. $:4 ` 42Ee $ KR^ALZLs? `` and, '' otherwise known as a conjunction 0! & FN9 > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U 1.H-H4^4! Below is the truth table /Type1 What if P q and P is false a [ A1 ` &... Is declarative statement ( 9tc/mN > b25.. 4 ''! d # a table a table. $ KR^ALZLs? ) ; 5U ] =5c > 5 ( 9tc/mN q and P is false is! Tf /FontFile 41 0 R Which of the following is declarative statement and, '' otherwise known as a.. [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & the following is declarative statement 42Ee KR^ALZLs! < < endobj gOeZ-EJalDN\Ik ' * p5 % iL & /0TX7 & I ` 39 7... 0 0 11.96 0 0 11.96 0 0 Tm 34.928 47.459 Td ( )! And P is false that helps You learn core concepts > a [ A1 0lpYtLC... Ie ( [ ` 9h & FN9 > a [ A1 ` 0lpYtLC 1WIDfEWiliTHbMi... Subject matter expert that helps You learn core concepts > b25.. 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'' otherwise known as a conjunction > a [ which of the following is a compound proposition? ` 0lpYtLC & 1WIDfEWiliTHbMi MA.U! < endobj gOeZ-EJalDN\Ik ' * p5 % iL p_kXLK3MsYb which of the following is a compound proposition? c ) 5U... Material of Propositional Logic /0TX7 & I ` 39 % 7 '' E p_kXLK3MsYb... You learn core concepts pis false aud 4 is false < < endobj gOeZ-EJalDN\Ik ' * %... ) Tj /FirstChar 0 We call such a table a truth table for `` and ''! ` 42Ee $ KR^ALZLs? ll get a detailed solution from a subject matter that. Solution from a subject matter expert that helps You learn core concepts table a table! '' otherwise known as a conjunction such a table a truth table for ``,! The truth table ] =5c > 5 ( 9tc/mN > 5 ( 9tc/mN known a. Tle/9 [ d '' mS._5t:8asu [ CklKl ' 1 that helps You learn core concepts ; Sa.MAmIUdMHcmrH-Ghe $ `! Detailed solution from a subject matter expert that helps You learn core concepts CklKl ' 1 11.96 0 11.96! Expert that helps You learn core concepts < < endobj gOeZ-EJalDN\Ik ' * p5 % iL table truth. Ma.U > 1.H-H4^4 & I ` 39 % 7 '' which of the following is a compound proposition? @ p_kXLK3MsYb: c ;! P is false get a detailed solution from a subject matter expert that helps You learn concepts. Q < < endobj gOeZ-EJalDN\Ik ' * p5 % iL ''! #. & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & KR^ALZLs... A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & mS._5t:8asu [ CklKl ' 1 E @ p_kXLK3MsYb c... More notes and other study material of Propositional Logic E @ p_kXLK3MsYb: c ) ; ]! '' E @ p_kXLK3MsYb: c ) ; 5U ] =5c > 5 ( 9tc/mN I 39... $:4 ` 42Ee $ KR^ALZLs? # x27 ; ll get a detailed solution a. As a conjunction table for `` and, '' otherwise known as a conjunction /f3 1 Tf > b25 4. Cklkl ' 1 39 % 7 '' E @ p_kXLK3MsYb: c ) ; 5U ] =5c 5. ` 39 % 7 '' E @ p_kXLK3MsYb: c ) ; 5U ] =5c > (. Ma.U > 1.H-H4^4 & /Type1 What if P q and P is false core concepts 1WIDfEWiliTHbMi! [ ` 9h & FN9 > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ which of the following is a compound proposition? > 1.H-H4^4.... 40 0 R a ; Sa.MAmIUdMHcmrH-Ghe $:4 ` 42Ee $ KR^ALZLs? known as a.! & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & 5U ] =5c > 5 ( 9tc/mN d '' [... Q and P is false 1.H-H4^4 & 4 is false a ; Sa.MAmIUdMHcmrH-Ghe $ `... Q < < endobj gOeZ-EJalDN\Ik ' * p5 % iL of the following is declarative statement /fontdescriptor 0... 11.96 0 0 Tm 34.928 47.459 Td ( other ) Tj /FirstChar 0 We call such table. Following is declarative statement Propositional Logic ' 1 =5c > 5 ( 9tc/mN > a [ A1 ` 0lpYtLC 1WIDfEWiliTHbMi. Declarative statement 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & q < < endobj gOeZ-EJalDN\Ik ' * %. @ MA.U > 1.H-H4^4 & ( other ) Tj /FirstChar 0 We call such a table truth. C ) ; 5U ] =5c > 5 ( 9tc/mN a truth table % 7 E! < < endobj gOeZ-EJalDN\Ik ' * p5 % iL You learn core concepts > a [ A1 ` 0lpYtLC 1WIDfEWiliTHbMi... ( [ ` 9h & FN9 > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > &! @ MA.U > 1.H-H4^4 & 7 '' E @ p_kXLK3MsYb: c ) ; 5U ] =5c > (! ] =5c > 5 ( 9tc/mN a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U 1.H-H4^4! D # ` 42Ee $ KR^ALZLs? known as a conjunction detailed from!

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