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

Write the following statement in the form of "if-then":
To get an $A^{+}$ in the class,it is necessary that you do all the exercises of the book.

Let $a : \sim (p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false,then the truth values of $a$ and $b$ are respectively:

Consider the following three statements:
$P: 5$ is a prime number.
$Q: 7$ is a factor of $192$.
$R: \text{L.C.M. of } 5 \text{ and } 7 \text{ is } 35$.
Then,the truth value of which one of the following statements is true?

Which of the following sentences are statements? Give reasons for your answer.
Mathematics is difficult.

What type of statement is $\sim (p \rightarrow q) \Leftrightarrow (\sim p \vee \sim q)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module