Boolean Simplification of $ (a+b) \cdot (a \cdot c + a \cdot \overline{c}) + a \cdot b + b $

Question

Below is my simplification, but my truth tables don't line up, but I can't find my error.

$ (a+b) \cdot (a \cdot c + a \cdot \overline{c}) + a \cdot b + b $

$ (a+b) \cdot a \cdot (c + \overline{c}) + a \cdot b + b $

$ (a+b) \cdot a + a \cdot b + b $

$ (a+b) \cdot a \cdot b $

Answer 1

I think that $a\cdot b + b = b$. So I think your fourth line should be $(a+b)\cdot a + b$.