Let A = {1,2,3} and R and S be two relations defined on A as follows: R = {(1,3), (3,2), (2,3), (3,3), (1,2)} S = {(1,1), (2,2),

Question

Let A = {1,2,3} and R and S be two relations defined on A as follows:
R = {(1,3), (3,2), (2,3), (3,3), (1,2)}
S = {(1,1), (2,2), (1,3), (2,1), (3,1), (1,2)}

Which of the following statements are correct?

I. R is transitive but S is not transitive.
II. R is not symmetric but S is symmetric.
III. Neither R nor S is antisymmetric.
IV. R U S is reflexive.
V. S - R is antisymmetric.

(A) II, III, IV and V
(B) I, II, III, IV and V
(C) I and III
(D) IV and V

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