Suppose x and y are real numbers and x = 2. Which of the following statements must be true about x and y?

Question

a. Both x and y must be rational.

b. Both x and y must be irrational.

c. Either x or y can be irrational but not both.

d. If either x or y is irrational then the other must also

be irrational.

Answer 1

You have not stated any relation between x and y, so I assume they are independent. x = 2 which is a rational number. We know nothing about y other than it is a real number. So y could be either rational or irrational.

a) cannot be true since y could be irrational

b) cannot be true because x is rational

c) could be true because y could be irrational but we know that x is not

d) cannot be true because y could be irrational but we know that x is not

Sounds as if c) is the best choice,.