If the truth values of p↔q and q↔r are T and F respectively, then the truth value of

Since ↔q and is true and q→r is false,therefore p and q are true andr is false. Then q∧r is also false. Thereforep→(q∧r), (p∧q)→r and (p→q)→r arefalse. Also since r → q is true,p→(r→q) is true

If the truth values of p↔q and q↔r are T and F respectively, then the truth value of

Since ↔q and is true and q→r is false,therefore p and q are true andr is false. Then q∧r is also false. Thereforep→(q∧r), (p∧q)→r and (p→q)→r arefalse. Also since r → q is true,p→(r→q) is true

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If the truth values of p $\leftrightarrow$ q and q $\leftrightarrow$ r are T and F respectively, then the truth value of

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$p \to (q \land r) is T$

$(p \land q) \to r is T$

$(p \to q) \to r is T$

$p \to (r \to q) is T$

answer is D.

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Detailed Solution

Since $\leftrightarrow$ q and is true and q $\to$ r is false,
therefore p and q are true and
r is false. Then $q \land r$ is also false. Therefore
$p \to (q \land r), (p \land q) \to r and (p \to q) \to r$ are
false. Also since r $\to$ q is true, $p \to (r \to q)$ is true