Boolean algebra Simplify the expression

Question

Simplify the expression using the rules in Boolean algebra. (a+b')(a'+b)(a+b)

Here's a list of the rules I got. enter image description here

My thinking is that the rule B18 is relevant here. But I can't get it to work.

Answer 1

You guess the rules: $$(a+b')(a'+b)(a+b) = (aa'+ab+b' a' +b'b)(a+b)=(ab+b'a')(a+b)=$$$$=aba + abb + b'a'a + b'a'b = ab+ab = ab$$