Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically equivalent to T. (619)]19

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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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
(pvq) v q by De Morgan's law
pv (q v 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 (pvq) v q by De Morgan's law pv (q v 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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