FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.5(i) Let A = {1, 2, 3, 4, 5}, B = {2, 3, 4, 6, 7}, C ={ 2, 4, 7, 8, 9}.
Then A ∪ B = {1, 2, 3, 4, 5, 6, 7}
and B ∪ A = {1, 2, 3, 4, 5, 6, 7}
∴ A ∪ B = B ∪ A (commutative law)
Again (A ∪ B) ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}
(B ∪ C) = {2, 3, 4, 6, 7, 8, 9}
A ∪ (B ∪ C) = {1, 2, 3, 4, 5, 6, 7, 8, 9}
∴(A ∪ B) C = A ∪ (B ∪ C) (associative law)
(ii) If A = {a, b, c, d}, B = (0}, C = φ, then
A ∪ B = {0, a, b, c, d},
A ∪ C = {a, b, c, d} = A and B ∪ C = {0}
Union of sets may be illustrated more clearly by using Venn Diagram as above.
The shaded region indicates the union of A and B i.e. A ∪ B
Intersection of Sets
If and B are two given sets, then their intersection is the set of those elements that belong to both A
and B, and is denoted by A ∩ B (read as A intersection of B or A cap B).
As for example :
(i) For the same sets A, B, C given in above example:
A ∩ B = { 2, 3, 4} here the elements 2,3,4, belong both to A and B; and
B ∩ A = { 2, 3, 4}
∴ A ∩ B = B ∩ A (commutative law).
(A ∩ B) ∩ C = {2, 4}
(B ∩ C) = {2, 4, 7}, A ∩ (B ∩ C) = {2, 4}
∴ (A ∩ B) ∩ C = A ∩ (B ∩ C) (associative law)
(ii) For the sets A, B, C given in example (ii) above,
A ∩ B = φ , B ∩ C = φ , A ∩ C = φ.
Intersection of two sets A and B is illustrated clearly by the Venn Diagram as given above
The shaded portion represents the intersection of A and B i.e., A∩ B
Disjoint Sets :