how x' + xy = x' + y ????

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x' + xy = x'(y+y') + xy

=x'y + x'y' + xy

=x'y + x'y + x'y' + xy (because AB+AB+AB+.......................=AB)

=(x'y + x'y') + (x'y + xy)

=x'(y+y') + y(x+x')

=x'+y

=x'y + x'y' + xy

=x'y + x'y + x'y' + xy (because AB+AB+AB+.......................=AB)

=(x'y + x'y') + (x'y + xy)

=x'(y+y') + y(x+x')

=x'+y

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