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2. The Well Ordering Principle (WOP): The Well Ordering Principle states that "any non empty subset of natural numbers must have a smallest element." Apply WOP to answer the following questions: a) Given a number n > 1, prove that the smallest divisor of n (divisor greater than 1) exists, and it is a prime number. b) Assume 'there cannot exist an infinitely long decreasing sequence of natural numbers'. Use this assumption to prove the WOP. That is, prove that any non-empty set S C N must have a smallest element. Hint: start a proof by contradiction; assume S has no smallest element. Since S / () choose s, E S. Since S has no smallest elements then si cannot be the smallest element of S ... Get a contradiction with the fact that there can't be an infinitely decreasing sequence of natural numbers