# Can you help me solve this Boolean algebra problem?

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1. Nov 18, 2016

### doktorwho

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. Nov 18, 2016

### LCKurtz

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