For any set A, prove that A⊆ϕ ⇔ A =ϕ

If A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 8} then find the universal set.

Prove that A ⊆B, B⊆ C and C⊆ A ⇒A = C.

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 = {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