Use Exercises 1 and 2 to give another proof that j.vvl = |-V||y| for all real numbers x an...

Use Exercises 1 and 2 to give another proof that j.vvl = |-V||y| for all real numbers x and y.

Exercise 1

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.

Exercise 2

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 1).