Mathematical Reasoning question bank (Maths)

The number of choices for $\Delta \in \left\{\wedge ,\vee ,\Rightarrow ,\iff \right\}$, such that $\left(p\Delta q\right)\Rightarrow \left(\left(p\Delta ~q\right)\vee \left(\left(~p\right)\Delta q\right)\right)$ is a tautology, is

The correct simplified circuit diagram for the logical statement $[\{\mathrm{q} \wedge(\sim \mathrm{q} \vee \mathrm{r})\} \wedge\{\sim \mathrm{p} \vee(\mathrm{p} \wedge \sim \mathrm{r})\}] \vee(\mathrm{p} \wedge \mathrm{r})$ where $\mathrm{p}, \mathrm{q}, \mathrm{r}$ represent switches $\mathrm{s}_1, \mathrm{~s}_2, \mathrm{~s}_3$ respectively.