# State whether the given statement is true of false:

Question:

State whether the given statement is true of false:

(i) The sum of two rationals is always rational.
(ii) The product of two rationals is always rational.
(iii) The sum of two irrationals is an irrational.
(iv) The product of two irrationals is an irrational.
(v) The sum of a rational and and irrational is irrational.
(vi) The product of a rational and an irrational is irrational.

Solution:

(i) True
(ii) True
(iii) False

Counter example: $2+\sqrt{3}$ and $2-\sqrt{3}$ are two irrational numbers. But their sum is 4, which is a rational number.

(iv) False

Counter example: $2 \sqrt{3}$ and $4 \sqrt{3}$ are two irrational number $s .$ B ut their product is 24, which is a rational number.

(v) True
(vi) True