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



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