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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that $q$ is false and $p \wedge q \leftrightarrow r$ is true.Since $q \equiv F$,then $p \wedge q \equiv F$.For the biconditional $p \wedge q

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given that $q$ is false and $p \wedge q \leftrightarrow r$ is true.Since $q \equiv F$,then $p \wedge q \equiv F$.For the biconditional $p \wedge q \leftrightarrow r$ to be true,$r$ must have the same truth value as $p \wedge q$.Therefore,$r \equiv F$.Now,let us evaluate the options:$(A)$ $p \vee r \equiv p \vee F \equiv p$,which is not a tautology.$(B)$ $(p \wedge r)$ $\rightarrow (p \vee r) \equiv (p \wedge F)$ $\rightarrow (p \vee F) \equiv F$ $\rightarrow p$. Since $F \rightarrow p$ is always true for any truth value of $p$,this is a tautology.$(C)$ $(p \vee r)$ $\rightarrow (p \wedge r) \equiv (p \vee F)$ $\rightarrow (p \wedge F) \equiv p$ $\rightarrow F$,which is not a tautology.$(D)$ $p \wedge r \equiv p \wedge F \equiv F$,which is a contradiction.

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

Similar Questions

If $p$ and $q$ are simple propositions,then $p \Leftrightarrow \sim q$ is true when

What is the statement $(p \wedge q) \rightarrow p$?

$ \sim[(\sim p) \wedge q] $ is logically equivalent to

The negation of the statement $q \wedge (\sim p \vee \sim r)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module