Intersection of Sets
If two sets A and B are given, then the intersection of A and B is the subset of universal set U, which consist of elements common to both A and B. It is denoted by the symbol ‘∩’. This operation is represented by:
A∩B = {x : x ∈ A and x ∈ B}
Where x is the common element of both sets A and B.
The intersection of sets A and B, can also be interpreted as:
A∩B = n(A) + n(B) – n(A∪B)
Where,
n(A) = cardinal number of set A,
n(B) = cardinal number of set B,
n(A∪B) = cardinal number of union of set A and B.
Example: Let A = {1,2,3} and B = {3,4,5}
Solution:
A ∩ B = {1,2,3} ∩ {3,4,5}
A ∩ B = {3}
Then, A ∩ B = {3}; because 3 is common to both the sets.
Venn Diagram of Intersection of sets
Example:
If A = {1, 2, 3, 4} and B = {3, 4, 5, 7}, then the intersection of A and B is given by A ∩ B = {3, 4}.