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Math Help - Prove that A x 0 = 0 Using Boolean Algerbra

  1. #1
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    Prove that A x 0 = 0 Using Boolean Algerbra

    Hi,

    I am trying to prove that A x 0 = 0 using Boolean Algebra.

    A x 0 = 0
    (A x 0) + (A x A') (Compliment multiplication)
    A x (0 + A') (Distributive Multiplication)
    A x A' (Identity addition)
    = 0 (Compliment multiplication)

    Is this correct? I assume that if a + 0 = a, a' + 0 = a', too.

    Thanks in advance!
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  2. #2
    MHF Contributor
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    Re: Prove that A x 0 = 0 Using Boolean Algerbra

    Hey SC313.

    Do you have to use certain laws to do the proof?

    The reason I ask is that A and 0 for any A = 0 by the truth table, and if you wanted to express it in an algebraic fashion, then this is simply A * B where A and B are in {0,1} which means the answer has to be zero either by the truth table or by this algebraic simplification.
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  3. #3
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    Re: Prove that A x 0 = 0 Using Boolean Algerbra

    I'm not 100% with this stuff, but that looks basically fine to me.

    The beginning of your derivation had some issues. Your first line (Ax0=0) isn't known, but is what you're trying to prove. Also, I'd insert a statement before your "Compliment Multiplication".

    So I'd maybe begin this way:
    A x 0
    = (A x 0) + 0 (Identity addition)
    = (A x 0) + (A x A') (Compliment multiplication)
    ...
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