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Simplifying Boolean Algebra

  1. Aug 8, 2016 #1
    The problem statement, all variables and given/known data
    (A OR C) AND NOT(C AND A AND B OR C AND A AND NOT B)
    or
    (A + C) (CAB + CAB')'

    Relevant Equations
    (A+B)' = A'B'
    A(B+C) = (AB) + (AC)
    (AB)' = A' + B'

    The attempt at a solution
    I'm not sure how I'm suppose to expand (CAB + CAB')' for simplifying. I keep arriving at false which shouldn't be the case.

    (A + C) (CA)' (B + B')' (I'm not sure if this is what your suppose to do)

    or

    (A + C) (C'A'B'C'A'B) (Not sure if i used (A+B)' = A'B' correctly)

    Thanks - Jay
     
    Last edited: Aug 8, 2016
  2. jcsd
  3. Aug 8, 2016 #2

    BvU

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    Hello Jaehyun, :welcome:

    Pity you deleted part of the template: relevant equations are needed to do what you want. List a few and you'll see which you need
     
  4. Aug 8, 2016 #3
    I'm confused on how this rule: (A+B)' = A'B' is used to help with (CAB + CAB')'.
     
  5. Aug 8, 2016 #4

    BvU

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    I was searching for (xyp + xyq) = xy (p+q)
     
  6. Aug 8, 2016 #5
    I don't think this rule would work as it leads to a false (CA)' (B + B')' = (CA)' (1)' = 0 unless this does not work for NOT.
     
  7. Aug 8, 2016 #6

    BvU

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    No. Do one step at a time.
     
  8. Aug 8, 2016 #7

    BvU

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    By the way, (XY)' ≠ X'Y' !
     
  9. Aug 8, 2016 #8
    (A + C) (CAB + CAB')'
    (A + C) (CA)' (B + B')'
    (A + C) (C' + A') (B + B')'
    (AC' + AA' + CC' + CA') (B + B')'
    (AC' + CA') (B + B')'

    So then (B + B')' = 0 meaning there is no simplified expression?
     
    Last edited: Aug 8, 2016
  10. Aug 8, 2016 #9

    BvU

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    My "I was searching for (xyp + xyq) = xy (p+q)" : was meant to lure you into (CAB + CAB') = CA(B+B') = CA

    (A + C) (CAB + CAB')' does NOT lead to (A + C) (CA)' (B + B')' !
     
  11. Aug 8, 2016 #10
    But (CAB + CAB') = CA(B+B') = CA is missing the NOT portion (CAB + CAB')'.

    Edit: I was rushing the question so much and I finally realised what I was doing wrong thanks BvU for putting up with me it's 2am where I live and I'm clearly not in the right mind at the moment. Solved.
     
    Last edited: Aug 8, 2016
  12. Aug 8, 2016 #11

    BvU

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    Yes. The NOT portion comes afterwards. (CA)' is easier to do than what you had before.

    Great. Advice: go a bit slower :smile: The speed will come with experience; in the beginning taking small steps and doing it right are more important.
     
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