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

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

Solution

$\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \mathrm{q}) \equiv \mathrm{F}$ We know that $\mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$ $\therefore \mathrm{p} \equiv \mathrm{T} \text { and }(\sim \mathrm{p} \vee 1) \equiv \mathrm{F}$ We know that $\mathrm{F} \vee \mathrm{F} \equiv \mathrm{F}$ $\therefore \sim \mathrm{p} \equiv \mathrm{F} \text { and } \mathrm{q} \equiv \mathrm{F}$ Thus p, q are T, F respectively.

Asked in: MHT CET 2021 (21 Sep Shift 2)

Practice more Mathematical Logic questions on Aicharya