Rational numbers are not closed under____________.

Which of the following is NOT a rational number?

Between two rational numbers(A) there is no rational number(B) there is exactly one rational number(C) there are infinitely many rational numbers(D) there are only rational numbers and no irrational numbers

The set of rational numbers has ........... and ...........  decimals*1 pointnon-terminating and repeatingterminating and non-repeatingterminating and repeatingnon-terminating and non-repeating

Decimal representation of a rational number cannot be(A) terminating(B) non-terminating(C) non-terminating repeating(D) non-terminating non-repeating

n each case below, either give an example of the desired object, or explainwhy no such object exists. Fully explain your answers.(a) A non-empty set of irrational numbers with rational supremum. [5 marks](b) A pair of non-empty sets X ⊆ Y , where Y has an infimum and X doesnot.