Question:
If $\mathrm{q}$ is false and $\mathrm{p} \wedge \mathrm{q} \leftrightarrow \mathrm{r}$ is true, then which one of the following statements is a tautology?
Correct Option: , 4
Solution:
Given $q$ is $F$ and $(p \wedge q) \leftrightarrow r$ is $T$
$\Rightarrow \mathrm{p} \wedge \mathrm{q}$ is $\mathrm{F}$ which implies that $\mathrm{r}$ is $\mathrm{F}$
$\Rightarrow \mathrm{q}$ is $\mathrm{F}$ and $\mathrm{r}$ is $\mathrm{F}$
$\Rightarrow(\mathrm{p} \wedge \mathrm{r})$ is always $F$
$\Rightarrow(\mathrm{p} \wedge \mathrm{r}) \rightarrow(\mathrm{p} \vee \mathrm{r})$ is tautology.