Mathematical Reasoning!

We can solve this using Boolean Algebra.

To solve this, we first need to know the Absorption Law, which states that $\text{A}.(\overline{\text{A}} + \text{B}) = \text{A}.\text{B}$ , which is trivially true. Taking the dual of it, we get the variant we need to solve this problem: $\text{A} + \overline{\text{A}}.\text{B} = \text{A} + \text{B}$ .

We convert $({\sim} s) \lor ({\sim} r \land s)$ into a Boolean expression: $\overline{s} + (\overline{r}.s)$

By Absorption Law, this is equivalent to $\overline{s} + \overline{r}$ .

If we negate that, then we get $\overline{\bar{s} + \bar{r}} = s + r = s \land r$ which follows from De Morgan's Law and the Involution Law.

Use Venn diagram considering r and s as intersecting sets in a universal set. Consider AND as intersection, OR as union and ~ as complement. Then take the complement the final region you get.