If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value ' $F$ ', then truth values of $p, q$ and…

If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value ' $F$ ', then truth values of $p, q$ and $r$ are respectively
  1. F,F,T
  2. T,T,T
  3. T,F,F
  4. F,F,F

Solution

$\because(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value $F$ $\Rightarrow(p \wedge \sim r)$ is $T$ and $(\sim p \vee q)$ is $F$ $\Rightarrow(P$ is $T$ and $\sim r$ is $T)$ and $(\sim p$ is $F$ and $q$ is $F)$ $\Rightarrow P$ is $T, r$ is $F$ and $q$ is $F$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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