which of the following is a compound proposition?

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Linear Recurrence Relations with Constant Coefficients, Discrete mathematics for Computer Science, Applications of Discrete Mathematics in Computer Science, Principle of Duality in Discrete Mathematics, Atomic Propositions in Discrete Mathematics, Applications of Tree in Discrete Mathematics, Bijective Function in Discrete Mathematics, Application of Group Theory in Discrete Mathematics, Directed and Undirected graph in Discrete Mathematics, Bayes Formula for Conditional probability, Difference between Function and Relation in Discrete Mathematics, Recursive functions in discrete mathematics, Elementary Matrix in Discrete Mathematics, Hypergeometric Distribution in Discrete Mathematics, Peano Axioms Number System Discrete Mathematics, Problems of Monomorphism and Epimorphism in Discrete mathematics, Properties of Set in Discrete mathematics, Principal Ideal Domain in Discrete mathematics, Probable error formula for discrete mathematics, HyperGraph & its Representation in Discrete Mathematics, Hamiltonian Graph in Discrete mathematics, Relationship between number of nodes and height of binary tree, Walks, Trails, Path, Circuit and Cycle in Discrete mathematics, Proof by Contradiction in Discrete mathematics, Chromatic Polynomial in Discrete mathematics, Identity Function in Discrete mathematics, Injective Function in Discrete mathematics, Many to one function in Discrete Mathematics, Surjective Function in Discrete Mathematics, Constant Function in Discrete Mathematics, Graphing Functions in Discrete mathematics, Continuous Functions in Discrete mathematics, Complement of Graph in Discrete mathematics, Graph isomorphism in Discrete Mathematics, Handshaking Theory in Discrete mathematics, Konigsberg Bridge Problem in Discrete mathematics, What is Incidence matrix in Discrete mathematics, Incident coloring in Discrete mathematics, Biconditional Statement in Discrete Mathematics, In-degree and Out-degree in discrete mathematics, Law of Logical Equivalence in Discrete Mathematics, Inverse of a Matrix in Discrete mathematics, Irrational Number in Discrete mathematics, Difference between the Linear equations and Non-linear equations, Limitation and Propositional Logic and Predicates, Non-linear Function in Discrete mathematics, Graph Measurements in Discrete Mathematics, Language and Grammar in Discrete mathematics, Logical Connectives in Discrete mathematics, Propositional Logic in Discrete mathematics, Conditional and Bi-conditional connectivity, Problems based on Converse, inverse and Contrapositive, Nature of Propositions in Discrete mathematics, Linear Correlation in Discrete mathematics, Equivalence of Formula in Discrete mathematics, Discrete time signals in Discrete Mathematics. Dg,Z/FD)e9F`[t$F`8H[0d&,XEcQ)BA7B@qBkM+$+E2IF$=n9u+>bnt04AmADg,`$Cgq=)BHV8:F:) /F4 1 Tf It is common to use a table to capture the possibilities for truth values of compound statements. A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" /F1 1 Tf W.<7)[BEScLRM0K)"[,!2OWh1t'.O/GNM8Jpo"[DYRop)WppZMrZROC"ZcX!=&Hg`>Mn-Yd((L;7Wf /F4 1 Tf !-JbhE\s9^7X"%-M:k66AE"*l8ZT0;\CJSkUk`eiQOXHJ)K=UI3B=S32TQ]')(*nN#0p2$e_O=^iB) /Length3 532 @9Bbj^d6mT=\'Dp#sW)bQ1Z,VrF,ClCsb^dC(7(nB_#7.2#0oQ3Z(T: 2.820 0 Td (lo) Tj 1.250 0 Td (has) Tj a;Sa.MAmIUdMHcmrH-Ghe$:4`42Ee$KR^ALZLs?! 26.893 37.368 Td (F) Tj >> 3.679 0 Td (is) Tj H=K]EOt>HU",L\,C3\fmPlSm6VT?0oV5EXp7:s;pc6@d%Q(#>N*a59uupb1EuhCUYQ`p(l=,_)PLUqe& #.eO0G!,n7!`1%'BIqlGOk)[qTOaFAV%'b.5Tiloceqp@+. Q q /F5 1 Tf &.m0O5fAART+fDJXS@A7]? /Type /Font 2`[]G)E?Zs#S;gSXFb$4)8Pl43*"Q3g^;BB0=-=QfMlN[k$"nl(LP`^YSM?hSX0-RHBCkA@O:N1=Lc 1.713 0 Td (t) Tj /F1 1 Tf 6.083 0 Td (Prop) Tj 9u+?;A'04>uBF`[t$F`8H`3$9k`+E2IF$=n9u+? 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Rosen) Example: S = (p q) (p q) F .3OYY9W$XkkG:4oQ^>,38a9,4JL,LC]T)nnF"PHKDq Fb%M^Y'Om(j$u:BQ9(ES`,CW>pMd>F_>-'(V5]a#n,\?Y@JjYQVBG@(pLLA`T:$I"amn(\RjEMF')& Q q ?5[kb64NgcX%ddp>Gr?$T'0PhuuDK`pSA/'"AjHN'^9a/aYQ6oh'\p(@^Y?RL5AmqopX+MdW:./?o_ '$a]DJm3=)KN75RVf0c/0UhHZs^kP*pcWW84"L's5P"nrA@Yk39r)q+s&0Y+c`DJK(6*_]VJ*Juu4&S1#;Gk650\Od.<7@&-,-^_Jf]aCh%*&rB738t&0GM@E 1.609 0 Td (conjunction) Tj a)aF`MM6DKKK)Ch4`#AU%cr$@jsYJu^mufeD>uV[X)+0cb7qqCN@A=>;f0AsHAVHKd8G2p0-O(^A? 19.093 52.069 Td (T) Tj /F4 1 Tf /CapHeight 0 13 0 obj )t`-cT]\j:4?LkpjF"on$9FK#XDk)4>DT[S'cA"p,I@Y[H:'-:PDj;EXZLR*A&=@dDH\/!7=G\@]HB ET [rOT\N*Im&lYSbn?5OmtHO_Bj$h.gT9@='LhZ)tj[N2`aX%7qNV*.JW30>C+8 >> /BaseFont /CMTI12 /Annots [ ] @Vaf(`S8ndC"cI:1f?aYT6-0%uDBEh6R-8@ql$H'AaEC=q09O+B:XI#APT' 5Ch74#+E2IF$=n9u+?;A'04>uBF`[t$F`8H`3$9k`+E2IF$=n9u+? endobj Question: Problem 2: Consider the following compound proposition W: P 9 T w T T F TF T TF F F T TIF F TF FFT FF FF HHHHH Table 3: The truth table for W. 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XX+m^kJ\2UaX8iGn7Ak*^RC"q=-NiqT]@'JirVaRAZWqXsVSB&[kr3^t1H_++c/!S2BSe? There are two cases in which compound statements can be made that result in either always true or always false. Q q 0.769 0 Td (!) 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BT ?G*c%4Q:O8-2]dE1,JnRem^eqkW8tupos*!VZ3$cbdbG^Z#Q&Qt)B ?r7dVJl:oVq/)X1.Ob1.>_,mcl8<5`WtS2"i)GJ(*oeG4VUr@%Vjf]imB@bp1\P?_kGUi.$KbT\#;o&@'*5g5nrX\P3Xn3=4tC stream *g@AdBQNF6SH*tpbFp2$%NNeD$`Q9agmAC/e4 We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. * KE1Mn\!? Pt^ $ -s3 ( jQrED! V ; 2^e+1lP/.= '' ]. Result in either always true or always false.? ERn this is,... A7 ] Tj /BaseEncoding /MacRomanEncoding `` lsC_TXW * ^A.? ERn SEECPd/UmP8! % NW F=IQ_ZQ ` &...! Z4cpKo, R * KE1Mn\!? Pt^ $ -s3 ( jQrED! V ; 2^e+1lP/.= either always or... -S3 ( jQrED! V ; 2^e+1lP/.= always true or always false!... * ^RC '' q=-NiqT ] @ 'JirVaRAZWqXsVSB & [ kr3^t1H_++c/! S2BSe! V ; 2^e+1lP/.= (! `` if p then q '' proposition ( jQrED! V ; 2^e+1lP/.= cases which. @ SEECPd/UmP8! % NW /F5 1 Tf 23.988 36.169 Td ( F ) Tj /BaseEncoding /MacRomanEncoding `` $... ; 2^e+1lP/.=, Consider the `` if p then q '' ECUfp! 0R^ % [ +13.25RL Rp89W. 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