gate level minimization

Question

prove that

x'y+xy'+xy=x+y

Answer 1

x'y+xy'+xy

x'y+x(y+y')...( Taking x common)

x'y'+x

(x'+x)(y+x)..(using distributive property)

x+y

Answer 2

RHS:

X'Y+XY'+XY

X'Y+X(Y+Y')

X'Y+X

X+Y             using(a+a'b=a+b)

RHS =LHS