. For each relation below on the set N = {1, 2, 3, .}

(i) is it reflexive? Symmetric? Transitive?

(If not, give example. For instance, (n,m): n

(ii) List all integers that are related to 6 (that is, list k such that (6,k) is in the relation)

(iii) Describe in English, as best you can the reflexive transitive closure of the relation

a. (n,m) : |m-n|=1 b. (n,m) such that gcd(n,m)>2 c. (n, m) : (n-m) mod 5 = 0