Which of the following statements is a tautol | vedclass

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(D) To check if $[p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$ is a tautology:$1$. Use the implication law $p \rightarrow q \equiv \sim p \vee q$:$[

Vedclass · Accepted Answer

$[p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$

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(D) To check if $[p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$ is a tautology:$1$. Use the implication law $p \rightarrow q \equiv \sim p \vee q$:$[p \wedge (\sim p \vee q)] \rightarrow q$$2$. Apply the distributive law:$[(p \wedge \sim p) \vee (p \wedge q)] \rightarrow q$$3$. Since $p \wedge \sim p \equiv F$ (contradiction):$[F \vee (p \wedge q)] \rightarrow q$$4$. Simplify using the identity law $F \vee r \equiv r$:$(p \wedge q) \rightarrow q$$5$. Apply the implication law again:$\sim (p \wedge q) \vee q$$6$. Apply De Morgan's law:$(\sim p \vee \sim q) \vee q$$7$. Use the associative law:$\sim p \vee (\sim q \vee q)$$8$. Since $\sim q \vee q \equiv T$ (tautology):$\sim p \vee T \equiv T$Since the result is $T$,the statement is a tautology.

Which of the following statements is a tautology?

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