Suppose S(n) is a predicate on natural numbers (Positive Integers), n and suppose
\\ This says that If S(k) is true then S(k+2) is also true.
Now, if above assertion holds then Consider the following statements:
S1 is true when S(n) is true for all n. S1 is false when S(n) is true for all n > 9. So, S1 may or may not hold.
S2 is always true. If there exists some n for which S(n) is true then S(n+2) , S(n+4), S(n+6) and so on will also be true. So, If there exists some n for which S(n) is true then for infinite number of natural numbers S(n) will be true hence we can say that For all n there exists some m>n such that S(m) is true.
So, S2 always holds.