# Boolean algebra: Logical equivalence

1. Feb 10, 2013

### Bipolarity

1. The problem statement, all variables and given/known data
I've been trying to prove the equivalence between the two statements for quite a while now, any ideas?

$$(A+C)(B+C') = BC + AC'$$

2. Relevant equations

3. The attempt at a solution
I used the distributive property to simplify the LHS to $$AB + BC + AC'$$
Unsure what to do next. Help is appreciated.

BiP

2. Feb 10, 2013

### I like Serena

Hi Bipolarity!

One way is to fill in all possible values for A and B.
That way you can proof they are equivalent.

Or if you want to do it by axioms:

AB+BC+AC' = AB(C+C') + BC + AC'
= ABC + ABC' + BC + AC'
= BC(A+1) + AC'(B+1)
= BC + AC'​