Write ‘T’ for true and ‘F’ for false for each of the following:

(i) Rational numbers are always closed under subtraction.

(ii) Rational numbers are always closed under division.

(iii)

(iv) Subtraction is commutative on rational numbers.

(v)

(i) true

Let there be two rational numbers and

Then,

which is also a rational number

Hence, Rational numbers are always closed under subtraction.

(ii) false

Hence, Rational numbers are not always closed under division.

(iii) false

Hence,

(iv) false

Let there be two rational numbers and

Then,

And

Therefore,

Hence, Subtraction is not commutative on rational numbers.

(v) true