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Boolean algebra: Logical equivalence

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data
    I've been trying to prove the equivalence between the two statements for quite a while now, any ideas?

    [tex] (A+C)(B+C') = BC + AC' [/tex]

    2. Relevant equations

    3. The attempt at a solution
    I used the distributive property to simplify the LHS to [tex] AB + BC + AC' [/tex]
    Unsure what to do next. Help is appreciated.

  2. jcsd
  3. Feb 10, 2013 #2

    I like Serena

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    Homework Helper

    Hi Bipolarity! :smile:

    One way is to fill in all possible values for A and B.
    That way you can proof they are equivalent.

    Or if you want to do it by axioms:

    AB+BC+AC' = AB(C+C') + BC + AC'
    = ABC + ABC' + BC + AC'
    = BC(A+1) + AC'(B+1)
    = BC + AC'​
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