Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically equivalent to T. [p^(p-q)] →q
Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically equivalent to T. [p^(p-q)] →q
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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Please help me with this. Complete the following be
![Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically
equivalent to T.
[p^ (p→q)] →q
(p vq) v q by De Morgan's law
pv (qv q) by associative law
(p^q) →q=(pq) v q by logical equivalence
(p ^ q) →q by identity law
(p ^ q) →q=[-p v (p→q)] v q by logical
equivalence
[pA (p→q)] → q
[p^ (p→q)] →q = [p^ (pv q)] →q by logical
equivalence
T by domination law
pv (qv q) by associative law
[F v (p ^ q)] →→q by negation law
[(p v p) ^ (pvq)] v q by distributive law](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F247d8035-87d8-4c44-a5de-dbb3e4e84ee6%2Fb3508523-35b6-4fba-8e91-b22925f28ee6%2F3n76w1o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically
equivalent to T.
[p^ (p→q)] →q
(p vq) v q by De Morgan's law
pv (qv q) by associative law
(p^q) →q=(pq) v q by logical equivalence
(p ^ q) →q by identity law
(p ^ q) →q=[-p v (p→q)] v q by logical
equivalence
[pA (p→q)] → q
[p^ (p→q)] →q = [p^ (pv q)] →q by logical
equivalence
T by domination law
pv (qv q) by associative law
[F v (p ^ q)] →→q by negation law
[(p v p) ^ (pvq)] v q by distributive law
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