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Use the laws of logic to show that $[(p \rightarrow q) \hat \ \ \ \sim q]\rightarrow \sim p$ is tautology.

written 9.0 years ago by teamques10 ★ 70k

modified 3.8 years ago by pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 4 Marks

Year: Dec 2013

discrete mathematics

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written 9.0 years ago by teamques10 ★ 70k

•   modified 9.0 years ago

Consider Truth table for above expression:

p	q	~p	~q	p->q	(p->q)^~q	[(p->q)^~q]->~p
T	T	F	F	T	F	T
T	F	F	T	F	F	T
F	T	T	F	T	F	T
F	F	T	T	T	T	T

Since in [(p->q)^~q]->~p, all the truth values are true (T), hence [(p->q)^~q]->~p is a tautology.

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