Let R = {(a, b) : a, b, ϵ N and a < b}.Show that R is a binary relation on N, which is neither reflexive nor symmetric. Show that R is transitive.

Let A = {3, 4, 5, 6} and R = {(a, b) : a, b ϵ A and a

(i) Write R in roster form.

(ii) Find: dom (R) and range (R)

(iii) Write R^{–1} in roster form

Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B.

Let R = {(x, x^{2}) : x is a prime number less than 10}.

(ii) Find dom (R) and range (R).

If A = {5} and B = {5, 6}, write down all possible subsets of A × B.