How to simplify the given boolean expression to simplest form?

Question

I have the expression xy+xy'z+x'yz'. I have tried a number of ways to simplify it. What approach will ensure that this expression is reduced to its simplest form?

Answer 1

$$ xy+xy'z+x'yz'=\\ xy(z+z')+xy'z+x'yz'=\\xyz+xyz'+xy'z+x'yz'=\\(xyz+xy'z)+(xyz'+x'yz')=\\xz(y+y')+yz'(x+x')=\\xz+yz'$$

Answer 2

I simplified it as $xz+yz'$ by constructing a Karnaugh map http://en.wikipedia.org/wiki/Karnaugh_map