If A = { a, b, c, d}, then a transitive relation on A among the following is

A

$$a: R_{1}=\left\{(a,a),(a,b),(b,a)\right\}$$

B

$$b: R_{2} = \left\{(a, a), (b, b), (c, d), (d, d), (a, c)\right\}$$

C

$$c: R_{3} =\left\{(a,a),(b,b),(a,b),(b,c)\right\}$$

D

$$d: R_{3} =\left\{(a,a),(a,b),(a,c),(a,d)\right\}$$