I have the the following logic function (where $'$ is NOT)
$f(a, b, c) = abc + ab'c + a'bc + a'b'c + ab'c'$
I have to simplify it as much as possible using only boolean algebra (no truth tables, Venn diagrams, etc.). So far I've managed to do the following
$= ab'(c'+c) + a'c(b+b') + abc$
$= ab' + a'c + abc$
I'm pretty sure it can be simplified further, but I'm not sure where to go from here.