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(D) The given statement is $A$ $\rightarrow (B$ $\rightarrow A)$.Using the implication law $p \rightarrow q \equiv \sim p \vee q$,we get:$A$ $\rightar

Vedclass · Accepted Answer

$A \rightarrow (A \vee B)$

Vedclass · Answer

(D) The given statement is $A$ $\rightarrow (B$ $\rightarrow A)$.Using the implication law $p \rightarrow q \equiv \sim p \vee q$,we get:$A$ $\rightarrow (B$ $\rightarrow A) \equiv \sim A \vee (\sim B \vee A)$By the associative and commutative laws:$\equiv (\sim A \vee A) \vee \sim B$$\equiv T \vee \sim B \equiv T$ (Tautology).Now,check the options for a tautology or equivalent form:Option $D$ is $A \rightarrow (A \vee B) \equiv \sim A \vee (A \vee B) \equiv (\sim A \vee A) \vee B \equiv T \vee B \equiv T$.Since both the original expression and option $D$ are tautologies,they are equivalent.

The statement $A$ $\rightarrow (B$ $\rightarrow A)$ is equivalent to

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