If a statement q has truth value False and (p | vedclass

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(D) Given that the truth value of $q$ is $False$ and $(p \wedge q) \leftrightarrow r$ is $True$.Since $q$ is $False$,the conjunction $(p \wedge q)$ is

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$(p \wedge r) \rightarrow (p \vee r)$

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(D) Given that the truth value of $q$ is $False$ and $(p \wedge q) \leftrightarrow r$ is $True$.Since $q$ is $False$,the conjunction $(p \wedge q)$ is always $False$ regardless of the truth value of $p$.Substituting this into the biconditional statement: $False \leftrightarrow r$ is $True$.For a biconditional statement to be $True$,both sides must have the same truth value. Therefore,$r$ must be $False$.Now,let us evaluate the options:$A) p \wedge q = p \wedge False = False$.$B) p \vee r = p \vee False = p$. This depends on $p$,so it is not necessarily $True$.$C) p \wedge r = p \wedge False = False$.$D) (p \wedge r)$ $\rightarrow (p \vee r) = (p \wedge False)$ $\rightarrow (p \vee False) = False$ $\rightarrow p$.Since $False \rightarrow p$ is always $True$ for any truth value of $p$,option $D$ is $True$.

If a statement $q$ has truth value $False$ and $(p \wedge q) \leftrightarrow r$ has truth value $True$,then which of the following has truth value $True$?

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