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

[rehcarlos]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[D H]

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

 

[rehcarlos]

Hey DH thanks for helping,

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

I need to know what's 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

 

[D H]

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).

 

[rehcarlos]

Got it! Thanks

 

[Bob]

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