State in each case, whether true or false :

(i) The sum of two rationals is a rational.

(ii) The sum of two irrationals is an irrational.

(iii) The product of two rationals is a rational.

(iv) The product of two irrationals is an irrational.

(v) The sum of a rational and an irrational is an irrational.

(vi) The product of a rational and an irrational is a rational.

(i) Adding two rational numbers will always result in rational number.

Hence, above statement is true.

(ii) Adding two irrational numbers can be rational as well as irrational.

Hence, above statement is false.

(iii) Multiplying two rational numbers will always result in rational number.

Hence, above statement is true.

(iv) Multiplying two irrational numbers can be rational as well as irrational.

Hence, above statement is false.

(v) Adding a rational and an irrational will always result irrational number.

Hence, above statement is true.

(iv) Multiplying a rational and an irrational can be rational as well as irrational.

Hence, above statement is false.