Chapter 18, Problem 27E

32. Prove that if is positive and is positive, then is positive.

Prove that the cancellation law for multiplication holds in Z. That is, if xy=xz and x0, then y=z.

Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of the semicircle on the hypotenuse is equal to the sum of the areas of the semicircles on the two legs.