Boolean algebra theorem question

AI Thread Summary
The Boolean algebra theorem A + notA * B = A + B has been verified using truth tables, but the derivation process is causing confusion. Following the professor's steps leads to a more complex expression rather than simplifying it. The discussion suggests that the derivation can be simplified significantly, proposing that it can be done in just two steps using known identities. The key identities mentioned are X + YZ = (X + Y)(X + Z) and X + X' = 1. The conclusion is that the derivation can be achieved more efficiently without the lengthy process initially attempted.
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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.
 
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No need for all this steps

You can do it in two steps

1) X+YZ = (X+Y)(X+Z)
2) X + X' = 1
 
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