Find R^–1, when

(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (4, 5)}

(ii) R = {(x, y) : x, y ϵ N, x + 2y = 8}.

Let A be the set of first five natural numbers and let R be a relation on A, defined by (x, y) ϵ R ↔ x ≤ y.

Express R and R^–1 as sets of ordered pairs.

Find: dom (R^–1) and range (R).

Let R = (x, y) : x, y ϵ Z and x² + y² = 25}.

Express R and R^–1 as sets of ordered pairs. Show that R = R^–1.

Let A = {a, b}. List all relation on A and find their number.

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.