When a dice is thrown, the sample space is given by S = {1, 2, 3, 4, 5, 6}.
Accordingly, we have:
(i) A = {1, 2, 3, 4, 5, 6}
(ii) B = Φ
(iii) C = {3, 6}
(iv) D = {1, 2, 3}
(v) E = {6}
(vi) F = {3, 4, 5, 6}
Here, A = {1, 2, 3, 4, 5, 6} and B = Φ
∴ A ∪ B = {1, 2, 3, 4, 5, 6}
Here, A = {1, 2, 3, 4, 5, 6} and B = Φ
∴ A ∩ B = Φ
Here, B = Φ and C = {3, 6}
∴ B ∩ C = Φ
Here, E = {6} and F = {3, 4, 5, 6}
∴ E ∩ F = {6}
Here, D = {1, 2, 3} and F = {3, 4, 5, 6}
∴ D ∩ F = {3}
Here, F = {3, 4, 5, 6} and S = {1, 2, 3, 4, 5, 6}
∴