(iii) A and C mutually exclusive?

S = {(1,1), (1, 2), (1, 3), (1,4), (1,5), (1,6), (2,1), (2, 2), (2, -3), (2, 4), (2,5), (2,6), (3,1), (3, 2), (3, 3), (3,4), (3,5), (3, 6), (4,1), (4,2), (4, 3), (4,4), (4, 5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5, 6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

A = {(3,6), (4,5),(4,6),(5,4),(5,5),(5,6), (6, 3), (6, 4), (6, 5), (6, 6)}

B = {(1,2), (2,2),(3,2),(4,2),(5,2),(6,2), (2,1), (2, 3), (2, 4), (2, 5), (2, 6)}

C = {(3, 6), (6, 3), (5, 4), (4, 5), (6, 6)}

A ∩ B = φ , B ∩ C = φ

A ∩ C = {(3,6), (6, 3), (5,4), (4, 5), (6, 6)}

(i) Yes, since A ∩ B = φ

(ii) Yes, since B ∩ C = φ

(iii) No, since A ∩ C ≠ φ.