Which of the following statement patterns is | vedclass

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(C) tautology is a statement pattern that is always true for all possible truth values of its components.Let us evaluate each option:$(A) \ p \vee (q

Vedclass · Accepted Answer

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

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(C) tautology is a statement pattern that is always true for all possible truth values of its components.Let us evaluate each option:$(A) \ p \vee (q \rightarrow p) \equiv p \vee (\sim q \vee p) \equiv (p \vee p) \vee \sim q \equiv p \vee \sim q$. This is not a tautology as it is false when $p$ is $F$ and $q$ is $T$.$(B) \ \sim q \rightarrow \sim p \equiv q \vee \sim p$. This is not a tautology as it is false when $q$ is $F$ and $p$ is $T$.$(D) \ p \wedge \sim p \equiv F$. This is a contradiction.$(C) \ (q \rightarrow p) \vee (\sim p \leftrightarrow q)$. Let us construct the truth table:$p, q$$(q \rightarrow p) \vee (\sim p \leftrightarrow q)$$T, T$$T \vee (F \leftrightarrow T) = T \vee F = T$$T, F$$T \vee (F \leftrightarrow F) = T \vee T = T$$F, T$$F \vee (T \leftrightarrow T) = F \vee T = T$$F, F$$T \vee (T \leftrightarrow F) = T \vee F = T$Since the result is always $T$,option $(C)$ is a tautology.

Which of the following statement patterns is a tautology?

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