Which of the following Boolean expressions is | vedclass

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Question

(A) We evaluate each expression using the identity $A \Rightarrow B \equiv \sim A \vee B$:$A) (\sim p$ $\Rightarrow q) \vee (\sim q$ $\Rightarrow p) \

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We evaluate each expression using the identity $A \Rightarrow B \equiv \sim A \vee B$:$A) (\sim p$ $\Rightarrow q) \vee (\sim q$ $\Rightarrow p) \equiv (p \vee q) \vee (q \vee p) \equiv p \vee q$. This is not a tautology as it depends on the truth values of $p$ and $q$.$B) (q$ $\Rightarrow p) \vee (\sim q$ $\Rightarrow p) \equiv (\sim q \vee p) \vee (q \vee p) \equiv (\sim q \vee q) \vee p \equiv T \vee p \equiv T$. This is a tautology.$C) (p$ $\Rightarrow q) \vee (\sim q$ $\Rightarrow p) \equiv (\sim p \vee q) \vee (q \vee p) \equiv (\sim p \vee p) \vee q \equiv T \vee q \equiv T$. This is a tautology.$D) (p$ $\Rightarrow \sim q) \vee (\sim q$ $\Rightarrow p) \equiv (\sim p \vee \sim q) \vee (q \vee p) \equiv (\sim p \vee p) \vee (\sim q \vee q) \equiv T \vee T \equiv T$. This is a tautology.Thus,the expression in option $A$ is not a tautology.

Which of the following Boolean expressions is not a tautology?

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