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

  1. Sep 4, 2013 #1
    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. jcsd
  3. Sep 4, 2013 #2

    D H

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    Expand (¬A)(C) on the right hand side as (¬A)(¬B)(C)+(¬A)(B)(C) and simplify.
     
  4. Sep 4, 2013 #3
    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
     
  5. Sep 4, 2013 #4

    D H

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    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).
     
  6. Sep 5, 2013 #5
    Got it! Thanks
     
  7. Sep 7, 2013 #6

    Bob

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    test
     
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