If q is false and p wedge q leftrightarrow r | vedclass

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(B) Given that $q$ is false $(F)$ and the statement $(p \wedge q) \leftrightarrow r$ is true $(T)$.Since $q$ is $F$,the conjunction $(p \wedge q)$ mus

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given that $q$ is false $(F)$ and the statement $(p \wedge q) \leftrightarrow r$ is true $(T)$.Since $q$ is $F$,the conjunction $(p \wedge q)$ must be $F$ regardless of the truth value of $p$.For the biconditional $(p \wedge q) \leftrightarrow r$ to be true,$r$ must have the same truth value as $(p \wedge q)$.Therefore,$r$ must be $F$.Now we evaluate the options with $q = F$ and $r = F$:Option $A$: $(p \vee F) 	o (p \wedge F) \equiv p 	o F \equiv 
eg p$. This is not a tautology.Option $B$: $(p \wedge F) 	o (p \vee F) \equiv F 	o p$. Since the antecedent is $F$,the implication is always $T$. Thus,it is a tautology.Option $C$: $p \wedge F \equiv F$. This is a contradiction.Option $D$: $p \vee F \equiv p$. This depends on the value of $p$.

If $q$ is false and $p \wedge q \leftrightarrow r$ is true,then which one of the following statements is a tautology?

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