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!

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.

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)

...