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Prove that the given proposition is logically equivalent to False. Apply appropriate laws of equivalences for proving. Provide handwritten solution following the table format provided. Upload a clear copy of the image, file should only be an image type or pdf. 1. (p → q)A -g) Ap= False Resulting propositions Applied Law of Equivalence You can refer to this example: Prove that -(p v-p Aql) = -p A-g Resulting propositions Applied Law of Equivalence by the De Morgan's law -p A--p) v-g) by the De Morgan's low by the double negation law -p A(p v-a) (-p Ap) vl-pA-a) by the distributive law by the negation law, becouse p Ap = F FV(-p1-a) by the commutative law by the identity law -p A-9 Use the following tables as references for the equivalences. TABLE 6 Logical Equivalences. Equivalence Name PAT=P Identity laws TABLE 8 Logical TABLE 7 Logical Equivalences

Prove that the given proposition is logically equivalent to False. Apply appropriate laws of equivalences for proving. Provide handwritten solution following the table format provided. Upload a clear copy of the image, file should only be an image type or pdf. 1. (p → q)A -g) Ap= False Resulting propositions Applied Law of Equivalence You can refer to this example: Prove that -(p v-p Aql) = -p A-g Resulting propositions Applied Law of Equivalence by the De Morgan's law -p A--p) v-g) by the De Morgan's low by the double negation law -p A(p v-a) (-p Ap) vl-pA-a) by the distributive law by the negation law, becouse p Ap = F FV(-p1-a) by the commutative law by the identity law -p A-9 Use the following tables as references for the equivalences. TABLE 6 Logical Equivalences. Equivalence Name PAT=P Identity laws TABLE 8 Logical TABLE 7 Logical Equivalences

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that the given proposition is logically equivalent to False. Apply appropriate laws of equivalences for proving. Provide handwritten solution following the table format provided. Upload a clear copy of the image, file should only be an image type or pdf. 1. ((p 9)A-q) Ap = False Resulting propositions Applied Law of Equivalence You can refer to this example: Prove that -(p v(-p 1g)) = -p A-q Resulting propositions Applied Law of Equivalence by the De Morgan's law by the De Morgan's law by the double niegation law -p 1-(-p Ag) -p A(-(-p) v-q) -p A(p v-g) (-pAp) vl-p -a) by the distributive law by the negation law, because -pAp = F Fv(-p1-g) by the commutative law (-p A-a) vF -p 1-9 by the identity law Use the following tables as references for the equivalences. TABLE 6 Logical Equivalences. Equivalence PAT= P Name Identity laws PVF= p TABLE 7 Logical Equivalences TABLE 8 Logical
Transcribed Image Text:Prove that the given proposition is logically equivalent to False. Apply appropriate laws of equivalences for proving. Provide handwritten solution following the table format provided. Upload a clear copy of the image, file should only be an image type or pdf. 1. ((p 9)A-q) Ap = False Resulting propositions Applied Law of Equivalence You can refer to this example: Prove that -(p v(-p 1g)) = -p A-q Resulting propositions Applied Law of Equivalence by the De Morgan's law by the De Morgan's law by the double niegation law -p 1-(-p Ag) -p A(-(-p) v-q) -p A(p v-g) (-pAp) vl-p -a) by the distributive law by the negation law, because -pAp = F Fv(-p1-g) by the commutative law (-p A-a) vF -p 1-9 by the identity law Use the following tables as references for the equivalences. TABLE 6 Logical Equivalences. Equivalence PAT= P Name Identity laws PVF= p TABLE 7 Logical Equivalences TABLE 8 Logical
PV (q Ar) = (Pv q)A (p vr) Distributive laws PA(q vr) = (p ^ q) v (par) (p r) A(q- r) = (p v q) -r -(pAq) =-p v n -(p v q) =-pA (p q) V (pr) = p (q vr) (p r) V (qr) = (p Aq)→r De Morgan's laws PV (pAq) = p Absorption laws PA(pvq) = P PV-p=T Negation laws PA-p=F
Transcribed Image Text:PV (q Ar) = (Pv q)A (p vr) Distributive laws PA(q vr) = (p ^ q) v (par) (p r) A(q- r) = (p v q) -r -(pAq) =-p v n -(p v q) =-pA (p q) V (pr) = p (q vr) (p r) V (qr) = (p Aq)→r De Morgan's laws PV (pAq) = p Absorption laws PA(pvq) = P PV-p=T Negation laws PA-p=F
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