I am trying to prove two boolean expressions by using algebraic simplification.

I am trying to prove:

1) ((-a -> -b) /\ (a != b)) \/ ((a /\ c) -> (b /\ c))

2) (if b then P else if b then Q else R) = (if b then P else R)

I have proved both using truth tables, but haven't yet using algebra.

I have tried, but keep going in circles back to the original expression. Any help would be great.

Thnks