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

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

Solution

Since $p \rightarrow q$ is false, when $p$ is true and $q$ is false. $\mathrm{p} \rightarrow(\mathrm{q} \vee \mathrm{r})$ is false, $\therefore \quad \mathrm{p}$ is true and $\mathrm{q} \vee \mathrm{r}$ is false $\Rightarrow p$ is true and both $q$ and $r$ are false.

Asked in: MHT CET 2024 (15 May Shift 1)

Practice more Mathematical Logic questions on Aicharya