2.2 Operations in Sets
(A) Union of two sets : The union of two sets A and B is the set which consists of all the elements of A and all the elements of B.
Let A = { 3, 4, 6, 7 } and B = { 4, 7, 9, 10 }
then A È B = { 3, 4, 6, 7, 9, 10 }
Read A È B as A union B
Thus A È B = { x  x Î A or x Î B or both } or
A È B = { x  x belong to at least one of the sets A and B }
The shaded region in the above figure shows A È B.We can easily see that AÈB = BÈ A. Obviously, for any set A, A È A = A and A È f = A
(B) Intersection of two sets : The intersection of two sets A and B is the set of common elements of A and B. We write such a set as A Ç B and read it as A intersection B. Symbolically,
A Ç B = { x  x ÎA and x Î B }
For example A = { 1, 2, 3, 4 } and B = { 2, 3, 4, 5, 6, 7 }
Then A Ç B = { 2, 3, 4 }
We can easily see that for any two sets, A and B
A Ç B = B Ç A
Also note that for any set A, A Ç A = A and A Ç f = f
The sets A and B are such that (see above figure) A Ç B = f, then A and B are called as disjoint sets.

Index
2.1 Sets
2.2 Operations on Sets
2.3 The Algebra of Sets
Chapter 3
