Expression to be reduced by using Boolean algebra

Question

Hi I have this expression XY'Z+YY'+X+XY'+XZ ( ' means not) Can anyone please show me the simplification of this expression? Thanks in advance.

This is what i got so far:

XY'Z+YY'+XY'+X(1+Z)
XY'Z+YY'+XY'+XY'+X
Y'(XZ+Y)+X(1+Y')  
Y'(XZ+Y)+X   

I know 1+Y=1 but 1+Y'=1 too?

Answer 1

Y'(XZ+Y)+X

change this back to:

XY'Z+YY'+X

Then simplify a bit:

XY'Z+YY'+X
YY' + X(1+Y'Z)
0 + X
X