Note: For all integers k,n it is true that kn, ktn, and k-n are integers. An integer k is even if and only if there exists an integer r such that k=2r. An integer k is odd if and only if there exists an integer r such that k=2r+1. For every integer k it is true that if k is even then k is not odd. For every integer k it is true that if k is odd then k is not even. For every integer k it is true that if k is not even then k is odd. For every integer k it is true that if k is not odd then k is even. If P then Q means the same thing as P - Q (P implies Q). Note that co-domain has the same meaning as codomain. For a finite set A such that the number of elements (members) of A is an integer n, the number of different subsets of A is 2". Definition: For sets A,B, a relation from A to B is a subset of the Cartesian product AxB. Definition: For a set A, a relation on A is a subset of the Cartesian product AXA. If A,B are finite sets such that An B is the empty set, and the integer r is the number of elements (members) of A, and the integer s is the number of elements (members) of B, then the number of elements (members) of AU B is r+s. Note: An B is the intersection of A and B. Note: AU B is the union of A and B. Note: The empty set is a set that does not have any element (member). Note: For a function f and sets A,B, f: A -> B has the same meaning as a function f from A to B, and the same meaning as a function f with domain A and codomain B. Definition: For an integer n and an integer k such that k#0, k divides n if and only if there exists an integer r such that n=rk.3. [25%] Let A={502,515,526,537,548,612,622,632,642} be a set. Let g be a function with domain A and codomain A such that the graph of g is a transitive relation on A, and such that g(526)-537. The graph of g is the relation on A defined by { (x,y) | x is an element (member) of A and y=g(x)}. Give the value of g(537), and prove that the value that you gave is correct