Answer to Question #259856 in Discrete Mathematics for Mehedi

Question

1. Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2,

0), (2, 2), and (3, 0). Find the

a) reflexive closure of R.

b) symmetric closure of R.

2. Find the transitive closures of these relations on {1, 2, 3, 4}.

a) {(1, 2), (2,1), (2,3), (3,4), (4,1)}

b) {(2, 1), (2,3), (3,1), (3,4), (4,1), (4, 3)}

c) {(1, 2), (1,3), (1,4), (2,3), (2,4), (3, 4)}

d) {(1, 1), (1,4), (2,1), (2,3), (3,1), (3, 2), (3,4), (4, 2)}

3. Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is

a) reflexive and transitive.

b) symmetric and transitive.

c) reflexive, symmetric, and transitive.