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

Which of the following sentences are statements? Give reasons for your answer.
The sum of $5$ and $7$ is greater than $10.$

Write the following statement in the form of "if-then":
The banana trees will bloom if it stays warm for a month.

The number of switches in the alternative equivalent simple circuit for the given circuit is:

Write the contrapositive and converse of the following statement:
"You cannot comprehend geometry if you do not know how to reason deductively."

The Boolean expression $(\sim(p \wedge q)) \vee q$ is equivalent to

Vedclass Test Series

Exam Paper Generator

Online Exam Module