Consider the following two propositions:P_1: | vedclass

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

Question

(C) Given the proposition $p \rightarrow ((\sim p) \vee q)$ is $FALSE$.An implication $A \rightarrow B$ is $FALSE$ only when $A$ is $TRUE$ and $B$ is

Vedclass · Accepted Answer

Both $P_1$ and $P_2$ are $FALSE$

Vedclass · Answer

(C) Given the proposition $p \rightarrow ((\sim p) \vee q)$ is $FALSE$.An implication $A \rightarrow B$ is $FALSE$ only when $A$ is $TRUE$ and $B$ is $FALSE$.Therefore,$p$ must be $TRUE$ and $((\sim p) \vee q)$ must be $FALSE$.Since $p$ is $TRUE$,$\sim p$ is $FALSE$.For $(\sim p \vee q)$ to be $FALSE$,both $\sim p$ and $q$ must be $FALSE$. Thus,$q$ is $FALSE$.Now,evaluate $P_1$ and $P_2$ for $p = TRUE, q = FALSE$:$P_1 = \sim(p$ $\rightarrow \sim q) = \sim(T$ $\rightarrow \sim F) = \sim(T$ $\rightarrow T) = \sim(T) = FALSE$.$P_2 = (p \wedge \sim q) \wedge ((\sim p) \vee q) = (T \wedge \sim F) \wedge ((\sim T) \vee F) = (T \wedge T) \wedge (F \vee F) = T \wedge F = FALSE$.Thus,both $P_1$ and $P_2$ are $FALSE$.

Consider the following two propositions:
$P_1: \sim( p \rightarrow \sim q )$
$P_2: ( p \wedge \sim q ) \wedge ((\sim p ) \vee q )$
If the proposition $p \rightarrow ((\sim p ) \vee q )$ is evaluated as $FALSE$,then

Similar Questions

If the truth value of the compound statement $[(p \vee q) \wedge (q \to r) \wedge (\sim r)] \to (p \wedge q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively......

Write the negation of the following statement:
$p:$ For every real number $x, x^{2} > x.$

Which of the following are pairs of equivalent circuits?

Check whether the following sentence is a statement. Give reasons for your answer.
$8$ is less than $6.$

Write the negation of the following statement:
$r:$ All birds have wings.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Consider the following two propositions:$P_1: \sim( p \rightarrow \sim q )$$P_2: ( p \wedge \sim q ) \wedge ((\sim p ) \vee q )$If the proposition $p \rightarrow ((\sim p ) \vee q )$ is evaluated as $FALSE$,then