# Why (NOT A)(NOT B)(C) + B = (NOT A)(C) + B [Boolean Algebra]

1. Sep 4, 2013

### rehcarlos

1. The problem statement, all variables and given/known data
I'm studying function simplification in boolean algebra, and I didnt understand the following step:
(NOT A)(NOT B)(C) + B = (NOT A)(C) + B

What happened to the NOT B?

2. Relevant equations
3. The attempt at a solution

2. Sep 4, 2013

### D H

Staff Emeritus
Expand (¬A)(C) on the right hand side as (¬A)(¬B)(C)+(¬A)(B)(C) and simplify.

3. Sep 4, 2013

### rehcarlos

Hey DH thanks for helping,

but I still don't get it, I mean...

I need to know whats the next step of (NOT A)(NOT B)(C) + B. In your answer, you are saying that I need to expand the right side... but in a real exercise, I wouldn't know what the right side would look like

4. Sep 4, 2013

### D H

Staff Emeritus
On the left hand side, then.

Expand B as B = (any boolean expression whatsoever)B + B. Here we'll use B = (¬A)(C)(B) + B. Then the left hand side becomes (¬A)(¬B)(C) + (¬A)(C)(B) + B. Combine the first two terms and simplify to yield (¬A)(C).

5. Sep 5, 2013

### rehcarlos

Got it! Thanks

6. Sep 7, 2013

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