Which of the following is false?

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

Question

(D) $1$. $p \rightarrow q \equiv \sim p \vee q$ is a standard logical equivalence.$2$. For $(p \vee q) \wedge (q \vee r)$ to be true,both $(p \vee q)$

Vedclass · Accepted Answer

The truth value of $p \wedge \sim (p \vee q)$ is always $T$.

Vedclass · Answer

(D) $1$. $p \rightarrow q \equiv \sim p \vee q$ is a standard logical equivalence.$2$. For $(p \vee q) \wedge (q \vee r)$ to be true,both $(p \vee q)$ and $(q \vee r)$ must be true. If $p=T, q=F, r=T$,then $(T \vee F) \wedge (F \vee T) = T \wedge T = T$. This is correct.$3$. By De Morgan's Law,$\sim (p \wedge (q \vee r)) \equiv \sim p \vee \sim (q \vee r) \equiv \sim p \vee (\sim q \wedge \sim r) \equiv (\sim p \vee \sim q) \wedge (\sim p \vee \sim r)$. This is correct.$4$. For $p \wedge \sim (p \vee q)$,we have $p \wedge (\sim p \wedge \sim q) \equiv (p \wedge \sim p) \wedge \sim q \equiv F \wedge \sim q \equiv F$. Thus,the statement that it is always $T$ is false.

Similar Questions

If the truth value of the Boolean expression $((p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r))$ $\rightarrow (p \wedge q)$ is false,then the truth values of the statements $p, q, r$ respectively can be:

Which of the following statements is a contradiction?

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

Which of the following sentences are statements? Give reasons for your answer.
The product of $(-1)$ and $8$ is $8.$

Which of the following statements is a tautology?

Vedclass Test Series

Exam Paper Generator

Online Exam Module