Discrete Structures for Computer Science

a. Let A = {0, 1, 2, 3, 4} and B = {a, b, c, d}. Then {(0, a), (0, b), (1, a), (2, b), (3, c), (4, d)}} is a relation from A to B. Represent the above relation using a diagram.

b. Which of the following relations, defined on {1, 2, 3, 4} are symmetric and which are antisymmetric, and which are reflective? R1 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 4), (4, 1), (4, 4)} R2 = {(1, 1), (1, 2), (2, 1)} R3 = {(1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 1), (4, 4)} R4 = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)} R5 = {(3, 4)} R6 = {(1, 1), (2, 2), (3, 3), (4, 4)}