EXERCISE 2.6.1: Rational and irrational numbers.

You can use the fact that √2 is irrational to answer the questions below. You can also use other facts proven within this

exercise.

(a) Prove that √2/2 is irrational.

(b) Prove that 2

2 is irrational.

(c) Is it true that the sum of two positive irrational numbers is also irrational? Prove your answer.

(d)

Is it true that the product of two irrational numbers is also irrational? Prove your answer.

(e)

Is the following statement true? Prove your answer.

If x is a non-zero rational number and y is an irrational number, then y/x is irrational.