Boolean algebra theorem question

[bcjochim07]

Homework Statement

My book contains this boolean algebra theorem:

A + notA * B = A + B

I have verified the validity of this statement using truth tables, but I find that I am unable to derive it. Our professor gave us a few steps to simplify Boolean expressions:

1) change all variables to their complements
2) change all ORs to ANDS and all ANDS to ORS simultaneously
3) take the complement of the entire expression

Homework Equations

The Attempt at a Solution

When I try to follow these steps, here's what happens:

step 1) A + notA * B => notA + A * notB
step 2) notA + A * notB => notA * A + notB
step 3) notA * A + notB +=> not(notA * A + notB)

and then breaking the longest bar using one of DeMorgan's theorems:

not(notA*A+notB) = not(notA*A) * not(notB) = not(0) * B = 1 * B = B

Maybe I'm making this more complicated than it is? What am doing wrong?

Thanks.

 

[Zayer]

No need for all this steps

You can do it in two steps

1) X+YZ = (X+Y)(X+Z)
2) X + X' = 1