If the statement (p rightarrow q) rightarrow | vedclass

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(D) For the implication $(p$ $\rightarrow q)$ $\rightarrow (q$ $\rightarrow r)$ to be false,the antecedent $(p \rightarrow q)$ must be true and the co

Vedclass · Accepted Answer

$F, T, F$

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(D) For the implication $(p$ $\rightarrow q)$ $\rightarrow (q$ $\rightarrow r)$ to be false,the antecedent $(p \rightarrow q)$ must be true and the consequent $(q \rightarrow r)$ must be false.For $(q \rightarrow r)$ to be false,$q$ must be true and $r$ must be false.Substituting $q = T$ into the antecedent $(p \rightarrow q)$,we get $(p \rightarrow T)$,which is always true regardless of the truth value of $p$.Thus,$p$ can be either true or false,$q$ must be true,and $r$ must be false.Comparing this with the options,the combination $(p, q, r) = (F, T, F)$ satisfies the condition.

If the statement $(p$ $\rightarrow q)$ $\rightarrow (q$ $\rightarrow r)$ is false,then the truth values of statements $p, q, r$ respectively,can be-

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