Which of the following is a tautology?

eSaral Updated on: 04 Jan, 2023

Question:
Which of the following is a tautology?

(1) $(\sim \mathrm{p}) \wedge(\mathrm{p} \vee \mathrm{q}) \rightarrow \mathrm{q}$
(2) $(\mathrm{q} \rightarrow \mathrm{p}) \vee \sim(\mathrm{p} \rightarrow \mathrm{q})$
(3) $(\sim \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{q}$
(4) $(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{p})$

Correct Option: 1

Solution:

Truth table

$\therefore(\mathrm{a}) \sim \mathrm{p} \wedge(\mathrm{p} \vee \mathrm{q}) \rightarrow \mathrm{q}$ be a tautology

Other options are not tautology.

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