I have been stuck on a homework problem which asks first to simplify a boolean equation using a k-map and second to reach the same result using boolean algerbra. The k-map was no issue and I have verified the k-map result, but no matter what I do, I am unable to achieve the same result using algerbra techniques. Any pointers would be much appreciated.
Original Equation: A'C (A'BD)' + A'BC'D' + AB'C
Kmap Solution: A'BD' + B'C
You have done everything correctly, but to get to the desired answer, let's pick it up a few lones earlier, where you have:
$B'C + A'CD' + A'BC'D'$
From here:
$= B'C + A'BCD' + A'B'CD' + A'BC'D'$ (By expansion of A'CD')
$= B'C + A'BCD' + A'BC'D'$ (Third term got Absorbed by first)
$= B'C + A'BD'$