expanding boolean expression as maxterm

Question

$$ F = A + B'C $$ The expression has bothered. I've tried to expand the expression in maxterm, however, I'm stuck on the $B'C $ part. My approach is like this $$ = A + (B'B) + (C'C) + B'C $$ $$ = (A + B')(A +B) + (C'C) + B'C $$ then, $$ = (A + B' + C')(A + B + C) + B'C $$ How can I convert $B'C $ part or can I ?

Answer 1

Ask for the inverse expression $F'$:

$$F' = (A' \land B) \lor (A' \land C')$$

In terms of a truth table this would be the set of all terms for $F = false$.

Then apply De Morgan's law to derive the required form.

The product-of-sums (or conjunctive normal form) for your expression is:

$$F = (A \lor B') \land (A \lor C)$$