<s>[INST] Simplifying from POS using boolean algeabra I have a boolean function, f  expressed in the Product of Sum form.
$$f = (A+B+C)\cdot(A+B+ \overline C)\cdot(\overline A + \overline B + \overline C) $$
On simplification I get, 
$$ f = ((A+B) + (C \cdot\overline C))\cdot (\overline A + \overline B + \overline C) $$
$$   = (A+B) \cdot (\overline A + \overline B + \overline C) $$
However, I do not know how to proceed after this step.  
The answer is given as $ (A+B)\cdot(A+\overline C)$
Any advice on how to proceed ?
 [/INST] Your answer is correct, while the given answer is incorrect (or there is a typo somewhere). Indeed, let $A = B = C = 1$. Then observe that:
\begin{align*}
f &= (A+B+C)\cdot(A+B+ \overline C)\cdot(\overline A + \overline B + \overline C) \\
&= (1 + 1 + 1) \cdot (1 + 1 + 0) \cdot (0 + 0 + 0) \\
&= 1 \cdot 1 \cdot 0 \\
&= 0
\end{align*}
while on the other hand, the proposed answer yields:
\begin{align*}
(A+B)\cdot(A+\overline C)
&= (1 + 1) \cdot (1 + 0) \\
&= 1 \cdot 1 \\
&= 1
\end{align*}
</s>