Verified answer

Truth table:

x y x+y x(x+y)

0 0 0 0

0 1 1 0

1 0 1 1

1 1 1 1

As first column and last column is same, it is proved.

This is direct boolean postulate known as redundancy law.

A(A+B)=A.

AA=A

0+A=A

1+A=1

We can prove like this

x(x+y)=xx+xy = x+xy

if x is zero then x+xy is zero as xy is also zero.

if x is 1 then x+xy is 1 independent of xy.

Thus, prooved

Redundancy Law Boolean Algebra