4 8 pts Show that the set S A 1 A c N and IA2 is count ably

(4) (8 pts) Show that the set S = {A 1 (A c N) and IA-2) is count- ably infinite (i.e. each element of S is a subset of N with exactly 2 elements).

Solution

Since S contains elements from natural numbers such that |A|=2

S = {-n,n: n is any natural number}

This will give say if n =1, S = {-1,1} and order 2.

Since n is infinite S will be countably infinite.