(a) A binary operation * is defined on the set of real numbers R by: x * y = x + y + 3xy, for all x, y ∈ R. (i) Show that the operation * is commutative. (ii) Show that the operation * is associative. (iii) Find the identity element e under the operation *. (iv) Find the inverse of an element x under the operation *. (b) A binary operation Δ is defined on the set S = {0, 1, 2, 3, 4} by x Δ y = (x + y) mod 5. (i) Construct a 5 × 5 operation table for Δ on S. (ii) Using your table, find the identity element for Δ on S. (iii) Find the inverse of each element in S under Δ. (iv) Determine whether S is closed under Δ, giving a reason for your answer.