Which of the following is not true?

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

Question

(A) We evaluate each option using truth tables:$(a)$ Let $x = (p \wedge \sim q)$ and $y = (p \rightarrow q)$. The truth table shows that $(x \leftrigh

Vedclass · Accepted Answer

$(p \wedge \sim q) \leftrightarrow (p \rightarrow q)$ is a tautology

Vedclass · Answer

(A) We evaluate each option using truth tables:$(a)$ Let $x = (p \wedge \sim q)$ and $y = (p \rightarrow q)$. The truth table shows that $(x \leftrightarrow y)$ is not a tautology (it is a contingency).$(b)$ This is a standard tautology known as the Law of Hypothetical Syllogism.$(c)$ This is a standard logical equivalence (Distributive Law of implication over conjunction).$(d)$ This is a standard logical equivalence for the negation of a biconditional statement.Therefore,option $(a)$ is not true.

Similar Questions

If $\sim p \lor q$ is false, then which of the following is correct?

The negation of the converse of the statement $p \lor q$ is:

The conditional $(p \wedge q) \Rightarrow p$ is :-

The logical statement $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to

The negation of the statement "$12$ is a multiple of $3$ and $12$ is a multiple of $4$" is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module