Categorize the following sets as countable or uncountable If

Categorize the following sets as countable or uncountable. If uncountable, does it have the
same cardinality as R?

(e) The set of all possible closed, bounded intervals in R where both endpoints are rational.

Details please...thanks

(b)Qu 2, 3) (c) on 2, 3) (d) 0, x 0, 1

A set is countable if it is finite or if it has sam e cardinality as the set of Natural numbers

(a)the set is a set of all irrational numbers hence it is not countable as the set of all irrational numbers are not countable

(b)The set of all rational numbers in union with [2,3) is countable as rational numbers are countable,

(c)the set of all rational numbers in intersection with [2 3) is a finite set hence countable

(d)Let A=[0,1] B=[0,1] here and B are countable hence AxB is countable