Consider x yz xy z for all x y z Is this statement True

Consider (x + y)z = x(y + z) for all x, y, z .

Is this statement True or Fale?

Solution

FALSE:

The statement true iff xz+yz= xy+yz

                               iff xz =xy for all x,y,z in Z.

Take x=1,y=2,z=3 . Then the equation is not satisfied.

So the statement is false.