Boolean algebra: Logical equivalence

[Bipolarity]

Homework Statement

I've been trying to prove the equivalence between the two statements for quite a while now, any ideas?

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

Homework Equations

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

 

[I like Serena]

Homework Statement

I've been trying to prove the equivalence between the two statements for quite a while now, any ideas?

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

Homework Equations

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

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'​