Boolean Algebra Identity

Discussion in 'Homework Help' started by j3lr0m, Oct 13, 2010.

  1. j3lr0m

    Thread Starter New Member

    Oct 13, 2010
    1
    0
    I've just started learning boolean algebra at university and am stuck by the following problem:

    Prove the identity a.b + a'.c = (a+c).(a'+b) using boolean algebra.

    Could somebody please give me a push in the right direction?

    Thanks in advance.
     
  2. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Why don't you make a truth table out of the right expression and solve it using a Karnaugh map. Boolean operations won't get you where you want easilly.
     
  3. Davit

    New Member

    Oct 14, 2010
    1
    0
    a.b + a'.c = (a+c).(a'+b)
    (a+c).(a'+b) = (a+c).a' + (a+c).b = a.a' + c.a' + a.b + c.b
    a.a' = F

    so (a+c).(a'+b) = F + c.a' + a.b + c.b = c.a' + a.b + c.b = a.b + a'.c + c.b= a.b + a'.c + c.b(a+a') = a.b + a'.c + c.b.a+c.b.a' = a.b + c.b.a+ a'.c +c.b.a' = a.b( 1 + c) + a'.c(1+b) =a.b + a'.c

    works both ways :)
     
  4. CMH70

    New Member

    Mar 11, 2010
    9
    0
    ummm...?? What ??????
     
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