State whether the following statements are true or false and Justify your statement.(i) Every rational number is a natural number.(ii) Irrational numbers are not real numbers.(iii) If you subtract a rational number from an irrational number is an irrational number.(iv) If we multiply two irrational numbers, the result is only irrational.(v) The addition of two irrational numbers always results in an irrational number.(vi) The sum of a rational number and an irrational number is irrational.(vii) Every real number is a rational number(viii) If you divide a rational number by an irrational number then you always get an irrational number.

(i) False. Every natural number is a rational number, but not every rational number is a natural number. For example, 1/2 is a rational number, but it is not a natural number.

(ii) False. Irrational numbers are real numbers. In fact, the set of real numbers includes both rational and irrational numbers.

(iii) True. If you subtract a rational number from an irrational number, the result is generally irrational. For example, if you subtract √2 (irrational) from 3 (rational), you get 3 - √2, which is still irrational.

(iv) False. If you multiply two irrational numbers, the result can be rational or irrational. For example, √2 (irrational) multiplied by √2 (irrational) equals 2 (rational).

(v) False. The addition of two irrational numbers can result in a rational number. For example, √2 (irrational) added to -√2 (also irrational) equals 0 (rational).

(vi) False. The sum of a rational number and an irrational number can be either rational or irrational, depending on the specific numbers involved. It is not always irrational.

(vii) False. Not every real number is a rational number. Irrational numbers, such as the square root of 2 or pi, are real numbers but not rational.

(viii) True. If you divide a rational number by an irrational number, the result is always irrational. This is because the division of a rational number by an irrational number leads to an expression that cannot be expressed as a fraction of two integers, making it irrational.