# identifying simplification rule

Discussion in 'Homework Help' started by metelskiy, Feb 2, 2011.

1. ### metelskiy Thread Starter Member

Oct 22, 2010
66
3
I dont really want to create a new thread for this simple question so I just found this thread that would correspond to my problem.
We are covering Boolean algebra right now and here is my problem:
$A \cdot \overline{A} \cdot B + A \cdot B \cdot \overline{C} + A \cdot B \cdot \overline{B}=A\cdot B\cdot \overline{C}$
I need to discover what rule has been used in this simplification but I don't see how could they achieve that output. Please help me to identify. Thanks.

Apr 20, 2004
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3. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Think about this: When a variable ${X}$ is 1, $\bar{X}$ is 0. When $\bar{X}$ is 1, ${X}$ is 0. And what is the result of 1 AND 0?

4. ### metelskiy Thread Starter Member

Oct 22, 2010
66
3
It just cleared in my mind that $A \cdot \bar{A} \cdot B=0$ and $A \cdot B\cdot\bar{B}=0$
Thanks Georacer, I used your tactic.