Let S be the subset of the set of ordered pairs of integers

defined recursively by

Basis step: (0, 0) ∈ S.

Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S

and (a + 3, b + 2) ∈ S.

a) List the elements of S produced by the first five applications

of the recursive definition.

How do I know which (a,b) pairs to use? I know that it's the first five but I don't know how to get the first five.