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

If $p \rightarrow(p \wedge \sim q)$ is false, then the truth values of $p$ and $q$ are respectively
  1. F, F
  2. $\mathrm{T}, \mathrm{F}$
  3. $\mathrm{F}, \mathrm{T}$
  4. $\mathrm{T}, \mathrm{T}$

Solution

$\mathrm{p} \rightarrow(\mathrm{p} \wedge \sim \mathrm{q})$ will be false if $\mathrm{P}$ is true and $\mathrm{p} \wedge \sim \mathrm{q}$ is false $\Rightarrow \mathrm{P}$ is true and $\mathrm{q}$ is true

Asked in: MHT CET 2022 (05 Aug Shift 2)

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