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Show that $[(p \rightarrow q) \hat \ \ \ \sim q]\rightarrow \sim p$ is tautology.
written 7.5 years ago by gravatar for teamques10 teamques10 ★ 66k modified 2.3 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: Dec 2015
discrete mathematics
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written 7.5 years ago by gravatar for teamques10 teamques10 ★ 66k

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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