Simplify expression in Boolean algebra

Question

In Boolean algebra, I need to prove that $AB+AB'C+BC'=AC+BC'$ and $(ABC)'(A+B+C)=A'B'C'$

Are both the questions correct?

Answer 1

No, both questions are not correct.

The first statement is a tautology.   You can prove it.

The second statement is not a tautology.   You can prove it is not always true. (via counter example)