Prove that the given proposition is logically equivalent to p. 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. pV(qA (-p→q)) = p Resulting propositions Applied Law of Equivalence Use the following tables as references for the equivalences. TABLE 6 Logical Equivalences. Equivalence Name PAT=P Identity laws pVF= p TABLE 7 Logical Equivalences Involving Conditional Statements. TABLE 8 Logical Equivalences Involving Biconditionals. pVT=T Domination laws PAF=F Pvp=p Idempotent laws P q =-p Vq p + q = (p q)^ (q → p) PAp=p d- e b = b +d Pvq =-p→9 -(-p) =P Double negation law p+q = -p ++ pvq =q vp Commutative laws P + q = (p^q) v(-p^¬q) -(p + q) = p → - p^q =-(p → -) (p- q) = p^ng (p vq) vr=pv (q vr) (paq)ar=PA (qAr) Associative laws pv (q ar) = (p v q)A (p vr) PA(q vr) = (png) v (par) (p 4)^(p →r) = p (q ^r) (p r)^(q r) = (p v q) → r Distributive laws -(png) = -p v-g (p v q) = -p A-g (p 4)v (p r) = p (q vr) (p r)V (q → r) = (p ^q) → r De Morgan's laws pv (pnq) = p PA(pvq) =p Absorption laws pv-p=T Negation laws PA-p=F
Prove that the given proposition is logically equivalent to p. 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. pV(qA (-p→q)) = p Resulting propositions Applied Law of Equivalence Use the following tables as references for the equivalences. TABLE 6 Logical Equivalences. Equivalence Name PAT=P Identity laws pVF= p TABLE 7 Logical Equivalences Involving Conditional Statements. TABLE 8 Logical Equivalences Involving Biconditionals. pVT=T Domination laws PAF=F Pvp=p Idempotent laws P q =-p Vq p + q = (p q)^ (q → p) PAp=p d- e b = b +d Pvq =-p→9 -(-p) =P Double negation law p+q = -p ++ pvq =q vp Commutative laws P + q = (p^q) v(-p^¬q) -(p + q) = p → - p^q =-(p → -) (p- q) = p^ng (p vq) vr=pv (q vr) (paq)ar=PA (qAr) Associative laws pv (q ar) = (p v q)A (p vr) PA(q vr) = (png) v (par) (p 4)^(p →r) = p (q ^r) (p r)^(q r) = (p v q) → r Distributive laws -(png) = -p v-g (p v q) = -p A-g (p 4)v (p r) = p (q vr) (p r)V (q → r) = (p ^q) → r De Morgan's laws pv (pnq) = p PA(pvq) =p Absorption laws pv-p=T Negation laws PA-p=F
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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Transcribed Image Text:Prove that the given proposition is logically equivalent to p. 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.
pV(q A (-p→-q)) = p
Resulting propositions
Applied Law of Equivalence
Use the following tables as references for the equivalences.
TABLE 6 Logical Equivalences.
Equivalence
Name
PAT=P
Identity laws
pvF=p
TABLE 7 Logical Equivalences
Involving Conditional Statements.
TABLE 8 Logical
Equivalences Involving
Biconditionals.
pVT T
Domination laws
PAF=F
PVp p
Idempotent laws
p q =¬p vq
PAp P
P q = (p9)^ (q→ P)
P q =¬9 → →P
Double negation law
p +q =-p +
d=(d-)-
Pvq -p-
Pvq qvp
Commutative laws
p q = (P^q)v (-p^¬q)
-(p q) = p → -g
p^q =¬(p→¬)
(pv q)vr=pv (q vr)
(p→ 9) = p ^ng
Associative laws
(pAq)Ar=pA(qAr)
(p 9) ^ (p → r) = p → (q ^r)
(p r)^(q→ r)= (p v q) → r
pv (qAr) = (p v q)pvr)
Distributive laws
PA(qvr) = (png)v (pAr)
De Morgan's laws
(p 4) v (p →r) = p (q vr)
-(p v q) =-pA
(p r)V(q→ r) = (p ^ q) →r
pv (pAq) = p
Absorption laws
PA(pvq) = p
pV-p T
Negation laws
PA-p= F
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