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Which of the following statement pattern is a tautology ?
(A) p \vee(q \rightarrow p)
(B) \sim q \rightarrow \sim p
(C) (q \rightarrow p) \vee(\sim p \leftrightarrow q)
(D) p \wedge \sim p
maths | Maths
Which of the following statement pattern is a tautology ?
(A) p \vee(q \rightarrow p)
(B) \sim q \rightarrow \sim p
(C) (q \rightarrow p) \vee(\sim p \leftrightarrow q)
(D) p \wedge \sim p

Correct option is

(C) (q \rightarrow p) \vee(\sim p \leftrightarrow q)

(A)

p \vee(q \rightarrow p) \equiv p \vee(\sim q \vee p) \equiv p \vee p \vee \sim q \equiv \mathrm{p} \vee \sim \mathrm{q}

(B) \sim \mathrm{q} \rightarrow \sim \mathrm{p} \equiv \mathrm{q} \vee \sim \mathrm{p}

(D) \mathrm{p} \wedge \sim \mathrm{p} \equiv \mathrm{F}

So left is (C)

i

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