need help simplifying boolean algebra exrpressions

Question

Can someone walk me through simplifying the following expression?

$$a\lnot b\lnot s + ab \lnot s + \lnot abs + abs$$

help and advice is appreciated!

Answer 1

As I see it, the first step is observing \begin{align*} (a \wedge \neg b \wedge \neg s) \vee (a \wedge b \wedge \neg s) & = (\neg s \wedge a) \wedge (\neg b \vee b) & \text{distrib., commut.} \\ &= (\neg s \wedge a) \wedge 1 & \text{complementation} \\ &= \neg s \wedge a & \text{identity} \end{align*} A similar simplification can be made to the right-hand side $(\neg a \wedge b \wedge s) \vee (a \wedge b \wedge s)$.

This leads me to $(\neg s \wedge a) \vee (b \wedge s)$ which doesn't seem to simplify more.