# Math Help - [SOLVED] Simplifying the boolean expression

1. ## [SOLVED] Simplifying the boolean expression

Anyone have an idea about how to even more simplify the following expression?

A'(A + B) + (B + AA)(A + B')

2. ## Boolean Algebra

Hello calltorahat
Originally Posted by calltorahat
Anyone have an idea about how to even more simplify the following expression?

A'(A + B) + (B + AA)(A + B')

Things to look out for when you're doing this sort of simplication:

$AA = A$ (1)

$A + A' = 1$ (2)

$AA' = 0$ (3)

The Distributive Law: $AB + AC = A(B+C)$ (4)

$A + 1 = 1$ (5)

$A.1 = A$ (6)

So, using (1):

$A'(A + B) + (B + AA)(A + B') = A'(A+B)+(B+A)(A+B')$

$= (A+B)(A'+A+B')$, using (4)

$= (A + B)(1)$, using (2) and (5)

$= A + B$, using (6)

(We didn't need (3) this time round.)