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# How to prove this Boolean theorem?

AB + A'C = (A + C) (A' + B)

Please explain. Thank you!

### 2 Answers

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- 8 years agoFavorite Answer
take, RHS:

(A + C) (A' + B) = AA'+AB+CA'+CB [here AA'=0],

=AB+CA'+CB(A+A') {Since, A+A'=1, BC=BC(A+A')}

=AB+A'C+ABC+A'BC (commutative & distributive)

=AB(1+C)+A'C(1+B) {since, 1+any = 1: 1+C =1, 1+B=1 }

=AB+A'C = LHS

- RogerLv 78 years ago
First expand (A + C) (A' + B) = AA' + A'C +BC +AB

But AA' =0

So (A+C)(A' +B) = A'C +AB +BC

not (A+C)(A' +B) = A'C +AB

Therefore

AB + A'C ≠ (A + C) (A' + B)

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