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Mathematical Reasoning
medium
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 $F$ ?
A
$P \vee Q \rightarrow \sim R$
B
$R \vee Q \rightarrow \sim P$
C
$\sim( P \vee Q ) \rightarrow \sim R$
D
$\sim( R \vee Q ) \rightarrow \sim P$
(JEE MAIN-2022)
Solution
$X \Rightarrow Y$ is a false
when $X$ is true and $Y$ is false
So, $P \rightarrow T , Q \rightarrow F , R \rightarrow F$
$(A)$ $P \vee Q \rightarrow \sim R$ is $T$
$(B)$ $R \vee Q \rightarrow \sim P$ is $T$
$(C)$ $\sim( P \vee Q ) \rightarrow \sim R$ is $T$
$(D)$ $\sim( R \vee Q ) \rightarrow \sim P$ is $F$
Standard 11
Mathematics
