Union on Sets
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol‘ ∪’ is used to denote the union. Symbolically, we write A ∪ B and usually read as‘ A union B’.
A ∪ B = { x: x ∈A or x ∈B } Numerical: Let A = { 2, 4, 6, 8 } and B = { 6, 8, 10, 12 }. Find A ∪ B.
Solution We have A ∪ B = { 2, 4, 6, 8, 10, 12 }
Note: Common elements 6 and 8 have been taken only once while writing A ∪ B. In the Venn diagram below, area in the green represents A ∪ B
Some Properties of the Operation of Union( i) A ∪ B = B ∪ A( Commutative law)( ii)( A ∪ B) ∪ C = A ∪( B ∪ C)( Associative law)( iii) A ∪ φ = A( Law of identity element, φ is the identity of ∪)( iv) A ∪ A = A( Idempotent law)( v) U ∪ A = U( Law of U) Intersection of Sets
The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol‘ ∩’ is used to denote the intersection.
The intersection of two sets A and B is the set of all those elements which belong to both A and B. Symbolically, we write A ∩ B = { x: x ∈ A and x ∈ B }.