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 ?
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*}
