Which of the following statements is a tautol | vedclass

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(A) statement is a tautology if its truth value is always $T$ for all possible truth values of its components.Let us analyze option $A$: $\sim(p \vee

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) statement is a tautology if its truth value is always $T$ for all possible truth values of its components.Let us analyze option $A$: $\sim(p \vee \sim q) \rightarrow (p \vee q)$.Using De Morgan's Law,$\sim(p \vee \sim q) \equiv \sim p \wedge q$.So,the expression becomes $(\sim p \wedge q) \rightarrow (p \vee q)$.This is equivalent to $\sim(\sim p \wedge q) \vee (p \vee q) \equiv (p \vee \sim q) \vee (p \vee q) \equiv p \vee (\sim q \vee q) \equiv p \vee T \equiv T$.Since the result is always $T$,the statement is a tautology.

Which of the following statements is a tautology?

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