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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
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 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
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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