12. Let S ={0, 1, 2, 4, 6}.

a. p ={(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (0, 1), (1, 2), (2, 4), (4, 6)}

b. p ={(0, 1), (1, 0), (2, 4), (4, 2), (4, 6), (6, 4)}

c. p ={(0, 1), (1, 2), (0, 2), (2, 0), (2, 1), (1, 0), (0, 0), (1, 1), (2, 2)}

d. p ={(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (4, 6), (6, 4)}

e. r = {} (empty set)

Find the reflexive, symmetric, and transitive closure of each of the relations in Exercise 12.