Let S Be the Set of Positive Integers $\in$

Essay

Let S be the set of positive integers defined by:
Basis step: 4 $\in$ S .
Recursive step: If n $\in$ S , then $5 n + 2 \in S$ and $5 n + 2 \in S$
(a) Show that if $n \in S$ , then $n \equiv 4$ (mod 6).
(b) Show that there exists an integer $m \equiv 4$ (mod 6) that does not belong to $S$