For any sets A and B, prove that:
(i) (A – B) ∩ B = ϕ
(ii) A ∪ (B – A) = A ∪ B
(iii) (A – B) ∪ (A ∩ B) = A
(iv) (A ∪ B) – B = A – B
(iv) A – (A ∪ B) = A – B
Two sets are shown with the following Venn Diagram
The yellow region is denoted by 1.
Blue region is denoted by 2.
The common region is denoted by 3.
(i) A - B denotes region 1
B denotes region (2+3)
So their intersection is a null set
(A - B)
B = ø
(ii) B - A denotes region 2
A denotes region (1+3)
So their union denotes region (1+2+3) which is the union of A and B
A
(B - A) = A
B
(iii) A - B denotes region 1
AB denotes region 3
Their union denotes region (1+3) which is set A(A - B)
(A
B) = A
(iv) AB denotes region (1+2+3)
(AUB) - B denotes region (1+2+3) - (2+3) = 1
A - B denotes region 1(A
B) - B = A - B
(v) Wrong question