# Thread: Prove that A x 0 = 0 Using Boolean Algerbra

1. ## 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)
= 0 (Compliment multiplication)

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

2. ## 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.

3. ## 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)
...

,

,

### x*0=0

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