I am working on some homework and I was wondering if I was able to do the following, I will show you all of the work I have done so far for the context, I am working on getting the complement of F.
$$ F=(a+c)(a+b')(a'+b+c')$$ $$ F=(a+b'c)(a'+b+c')\rightarrow(A+B)(A+C)=A+BC$$ $$ F'=\overline{(a+b'c)}+\overline{(a'+b+c')}\rightarrow DeMorgans$$
After all of that I am left with what is below,
$$(a'c' +a'b + abc')$$
I'm asking because I know that $\overline{w}y + wy = y$ but I do not know if I can apply that here in the following way,
$$ (a'c' +a'b + abc')= a'c'+c$$
I know that the simplified version of $F=a$ meaning that the simplified version of $F'=a'$, and if I can apply the following above then $F'$ will equal $a'$
Sorry if this is confusing, I tried my best to explain it.