Determine whether each statement is true or false. For a real number x, x · 0 = x.

For a real number x where x ≠ 0, x () = 1.

For two different real numbers x and y, |x - y| = |x + y|.

For real numbers x, y, and z, (x + y)(z) = (xz) - (yz).

For rational numbers x and y, where y ≠ 0 is always a rational number.