Thread: Please help me answer the querry #1 i have posted. (order relation)

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.

Originally Posted by jakeshinryu

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).

Set elements should be surrounded by curly braces, not by parentheses.

Let's consider the set {2, 3}. Are you really asking if this set is finite and the greatest common divisor of its elements is 1? If so, then do you know what the the greatest common divisor is? If so, then what exactly is your difficulty? If you know whether {2, 3} is in A, then which set from (a) presents a problem?