Some more deductions/theorems/ related to operations on sets

If A and B are two sets

(i) A – B = A ∩ B’
(ii) B – A = B ∩ A’
(iii) A – B = A <=> A ∩ B = ф
(iv) (A – B) U B = A U B
(v) (A-B) ∩ B = ф
(vi) A is a sub set of B <=> B’ is a subset of A’
(vii) (A-B) U (B-A) = (A U B) – (A ∩ B)

If A, B and C are three sets, then

(i) A – (B ∩ C) = (A-B) U (A-C)
(ii) A – (B U C) = (A-B) ∩ (A-C)
(iii) A ∩ (B-C) = (A ∩ B) - (A ∩ C)
(iv) A ∩ (B Δ C) = (A∩B) Δ (A∩C)