If $p, q, r$ are simple propositions with truth values $\mathrm{T}, \mathrm{F}, \mathrm{T}$, then the truth…

If $p, q, r$ are simple propositions with truth values $\mathrm{T}, \mathrm{F}, \mathrm{T}$, then the truth value of $(\sim p \vee \mathrm{q}) \wedge \sim r$ $\Rightarrow p$ is
  1. true
  2. false
  3. true, if $r$ is false
  4. true, if $q$ is true

Solution

$\sim \mathrm{p} \vee \mathrm{q}$ means $\mathrm{F} \vee \mathrm{F}=\mathrm{F}, \sim \mathrm{r}$ means $\mathrm{F}$
$\therefore \quad[(\sim \mathrm{p} \vee \mathrm{q}) \wedge \sim \mathrm{r}] \Rightarrow \mathrm{p}$ means $\mathrm{T}$

Asked in: TEST SERIES MHT-CET Full Test 6

Practice more Mathematical Logic questions on Aicharya