Show that the set of all finite subsets of the set of positive integers is a countable set.

Solution :Step 1:In this problem, we have to show that the set of all finite subset of the set of a positive integer is countable.Step 2:The definition of the countable set:Now a set S is countable if there exists an injective function f : SN, (where N is the set of natural number).That is a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.