Use proof by cases to prove that sgn(xy) = sgn(x)sgn(y) for all real numbers. x and y (sgn...

Use proof by cases to prove that sgn(xy) = sgn(x)sgn(y) for all real numbers. x and y (sgn is defined in Exercise).

Exercise

Define the sign of the real number x. sgn(x), as

Use proof by cases to prove that | x | = sgn(x)x for every real number x.