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

Statement-$I$: $\sim (p \leftrightarrow q)$ is equivalent to $(p \wedge \sim q) \vee (q \wedge \sim p)$.
Statement-$II$: $p$ $\rightarrow (p$ $\rightarrow q)$ is a tautology.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$

Which of the following sentences are statements? Give reasons for your answer.
"The sides of a quadrilateral have equal length."

Show that the statement $p:$ "If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$" is true by the direct method.

Vedclass Test Series

Exam Paper Generator

Online Exam Module