In Example 4.12, Exercise 4.36, and Exercise 4.37, we proved that if x and y are both rational, then so are all three of xy, x − y, and x y . The converse of each of these three statements is false....

In Example 4.12, Exercise 4.36, and Exercise 4.37, we proved that if x and y are both rational, then so are all three of xy, x − y, and x y . The converse of each of these three statements is false. Disprove the following claims by giving counterexample

1 If xy is rational, then x and y are rational.

2 If x − y is rational, then x and y are rational.

Exercise 4.37

If x and y are rational numbers and y 6= 0, then x y is also rational