If $\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \mathrm{q})$ is false, then the truth values of $\mathrm{p}$…

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

Solution

We know that $\mathrm{T} \rightarrow \mathrm{F}$ is false. $\therefore \mathrm{p}$ must be true and $(\sim \mathrm{p} \vee \mathrm{q})$ must be false. $\Rightarrow \mathrm{p}$ is true. We know that $\mathrm{F} \vee \mathrm{F}$ is false. So $\mathrm{q}$ must be false.

Asked in: MHT CET 2020 (16 Oct Shift 1)

Practice more Mathematical Logic questions on Aicharya