1. Let A be the family of all subsets A of the natural numbers N where A has the following properties: A is finite and the greatest common divisor of the elements of A is 1.

a. State whether or not each of the following subsets of N belongs to A: (2,3,8),(2,3,5,8),(2,5),2,3,4,5,...),(4,6,8) and (2,3).

b. Order A by set inclusion, that is, X precedes Y if X is a subset of Y, and let B be the subfamily of A which consists of the sets in (a) which belongs to A. Construct a diagram of B.