If A = {a, b, c, d, e, f}, B = {c, e, g, h} and C = {a, e, m, n}, find:

(i) A ∪ B

(ii) B ∪ C

(iii) B ∪ C

(iv) C ∩ A

(vi) A ∩ B

For any set A, prove that A⊆ϕ ⇔ A =ϕ

State whether the given statement is true false:

(i) If A ⊂ B and x∉B than x ∉A.

(ii) If A ⊆ϕ then A = ϕ

(iii) If A, B and C are three sets such than A ϵ B and B ⊂ C then A ⊂ C.

(iv) If A, B and C are three sets such than A ⊂B and B ϵ C then A ϵC.

(v) If A, B and C are three sets such that A ⊄B and B ⊄C then A ⊄C.

(vi) If A and B are sets such that x A and A ϵ B then x ϵ B.

If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8} and C = {10, 11, 12, 13, 14}, find:

(i) A ∪ B

(ii) B ∪ C

(iii) A ∪ C

(iv) B ∪ D

(v) (A ∪ B) ∪ C

(vi) (A ∪B) ∩C

(vii) (A ∩ B) ∪D

(viii) (A ∩ B) ∪ (B ∩ C)

(ix) (A ∩ C) ∩ (C ∪ D

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13} and C = {11, 13, 15}, and D = {15, 17}, find:

(i) A ∩ B

(ii) A ∩ C

(iii) B ∩ C

(iv) B ∩ D

(v) B ∩ (C ∪ D)

(vi) A ∩ (B ∪ C)