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