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Can you help me solve this Boolean algebra problem?

  1. Nov 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Prove that $$(\bar{a} + b)(b+c) + a\bar{b}$$ where ##a,b## can be from the set ##B\in\{0, 1\}## equals $$a+b+c$$

    2. Relevant equations
    Rules of Boolean Algebra
    3. The attempt at a solution

    My attempt:
    ##\bar{a}b + \bar{a}c + bb + bc + a\bar{b}##
    ##b(\bar{a} + 1+c) + \bar{a}c + a\bar{b}##
    ##b +\bar{a}c + a\bar{b}##
    ##b(\bar{a} + a) + \bar{a}c + a\bar{b}##
    ##b\bar{a} +ba + \bar{a}c + a\bar{b}##
    ##b\bar{a} + a + \bar{a}c##
    and am stuck, cant get rid of these ##\bar{a}, \bar{b}##, could you help?
     
  2. jcsd
  3. Nov 18, 2016 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Try using ##a + \bar a b = a +b## a couple of times.
     
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