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

In a Boolean Algebra $B$,for all $x, y \in B$,$x \wedge (x \vee y)$ is equal to

The symbolic form of the following circuit is (where $p, q$ and $r$ represent switches $s_{1}, s_{2}$ and $s_{3}$ which are closed respectively):

If $p, q, r$ are simple propositions with truth values $T, F, T$ respectively, then which of the following is not a true statement?

Which of the following statements is/are False?
$S_1 : \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2 : \exists x \in N$, such that $x - 17 < 20$.
$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.
$S_4 : \forall n \in N, n^2 \ge 1$.

The conditional statement $(p \wedge q) \implies p$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module