Can you help me solve this Boolean algebra problem?

[doktorwho]

Homework Statement

Prove that $$(\bar{a} + b)(b+c) + a\bar{b}$$ where $a,b$ can be from the set $B\in\{0, 1\}$ equals $$a+b+c$$

Homework Equations

Rules of Boolean Algebra
3. The Attempt at a Solution [/B]
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, can't get rid of these $\bar{a}, \bar{b}$, could you help?

 

[LCKurtz]

Homework Statement

Prove that $$(\bar{a} + b)(b+c) + a\bar{b}$$ where $a,b$ can be from the set $B\in\{0, 1\}$ equals $$a+b+c$$

Homework Equations

Rules of Boolean Algebra
3. The Attempt at a Solution [/B]
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, can't get rid of these $\bar{a}, \bar{b}$, could you help?

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