Let p, q, r be three logical statements. Cons | vedclass

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

Question

(C) Given $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$.Using the associative and idempotent laws,we have $S_{1} \equiv (\sim p \vee \sim p) \vee

Vedclass · Accepted Answer

If $S_{2}$ is False,then $S_{1}$ is True

Vedclass · Answer

(C) Given $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$.Using the associative and idempotent laws,we have $S_{1} \equiv (\sim p \vee \sim p) \vee (q \vee r) \equiv \sim p \vee (q \vee r)$.Given $S_{2}: p \rightarrow (q \vee r)$.Using the conditional law $p \rightarrow x \equiv \sim p \vee x$,we have $S_{2} \equiv \sim p \vee (q \vee r)$.Since $S_{1} \equiv S_{2}$,they always have the same truth value.Therefore,if $S_{2}$ is False,$S_{1}$ must also be False.Thus,the statement 'If $S_{2}$ is False,then $S_{1}$ is True' is $NOT$ true.

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

Similar Questions

The negation of the statement "The number is an odd number if and only if it is divisible by $3$."

If $p: \forall n \in N, n^2+n$ is an even number and $q: \forall n \in N, n^2-n$ is an odd number,then the truth values of $p \wedge q, p \vee q$ and $p \rightarrow q$ are respectively:

Let $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta ((p \vee q) \Rightarrow q)$ is a tautology. Then $\Delta$ is equal to

Which of the following Boolean expressions is a tautology?

If $p \rightarrow (p \wedge \neg q)$ is false,then the truth values of $p$ and $q$ are respectively

Vedclass Test Series

Exam Paper Generator

Online Exam Module