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 }.