How to prove this Boolean theorem?

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

Please explain. Thank you!

2 Answers

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  • 7 years ago
    Favorite 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

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  • Roger
    Lv 7
    7 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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