If the truth value of the statement (P wedge | vedclass

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

Question

(D) The implication $X \rightarrow Y$ is $F$ if and only if $X$ is $T$ and $Y$ is $F$.Given $(P \wedge (\sim R)) \rightarrow ((\sim R) \wedge Q)$ is $

Vedclass · Accepted Answer

$\sim(R \vee Q) \rightarrow \sim P$

Vedclass · Answer

(D) The implication $X \rightarrow Y$ is $F$ if and only if $X$ is $T$ and $Y$ is $F$.Given $(P \wedge (\sim R)) \rightarrow ((\sim R) \wedge Q)$ is $F$,we have:$P \wedge (\sim R) = T \implies P = T$ and $\sim R = T \implies R = F$.$(\sim R) \wedge Q = F$. Since $\sim R = T$,we must have $Q = F$.So,the truth values are $P = T, Q = F, R = F$.Now,check the options:$(A) P \vee Q$ $\rightarrow \sim R = (T \vee F)$ $\rightarrow T = T$ $\rightarrow T = T$.$(B) R \vee Q$ $\rightarrow \sim P = (F \vee F)$ $\rightarrow F = F$ $\rightarrow F = T$.$(C) \sim(P \vee Q)$ $\rightarrow \sim R = \sim(T \vee F)$ $\rightarrow T = \sim T$ $\rightarrow T = F$ $\rightarrow T = T$.$(D) \sim(R \vee Q)$ $\rightarrow \sim P = \sim(F \vee F)$ $\rightarrow F = \sim F$ $\rightarrow F = T$ $\rightarrow F = F$.Thus,the statement in option $(D)$ is $F$.

If the truth value of the statement $(P \wedge (\sim R)) \rightarrow ((\sim R) \wedge Q)$ is $F$,then the truth value of which of the following is $F$?

Similar Questions

The inverse of the proposition $(p \wedge \sim q) \rightarrow r$ is:

Rewrite the following statement using "if-then" in five different ways conveying the same meaning:
"If a natural number is odd,then its square is also odd."

$(p \wedge \sim q \wedge \sim r) \vee (\sim p \wedge q \wedge \sim r) \vee (\sim p \wedge \sim q \wedge r)$ is equivalent to-

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

Negation of the statement: $\sqrt{5}$ is an integer or $5$ is irrational is

Vedclass Test Series

Exam Paper Generator

Online Exam Module