$p$ and $q$ are two logical statements. If $r: p \rightarrow(\sim p \vee q)$ has truth value false, then…

$p$ and $q$ are two logical statements. If $r: p \rightarrow(\sim p \vee q)$ has truth value false, then truth values of $p$ and $q$ are respectively
  1. $\mathrm{T}, \mathrm{T}$
  2. $\mathrm{T}, \mathrm{F}$
  3. $\mathrm{F}, \mathrm{T}$
  4. F, F

Solution

$p \rightarrow(\sim p \vee q)$ is false $\Rightarrow(p$ is true $)$ and $(\sim p \vee q)$ is false $\Rightarrow p$ is true and $q$ is false

Asked in: MHT CET 2022 (10 Aug Shift 1)

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