In this page,
we are going to know the "Intersection of sets"
There are Three Basic operations in sets. Those are Union of sets, intersection of sets and difference of sets.
In the last post , we discussed about "Union of sets"
Before going to know the operations on sets
first we know the Introduction of sets and Types of sets
Now let us learn,
Intersection of two sets:
Let A and B are two non-empty sets.
"A set with common elements of set A and Set B is called Intersection set of set A and set B". (Common element means the element belongs to both sets)
It is denoted as "A∩B".
Read as "A intersection B".
Set builder form of A∩B is { x/ x𝜖A and x𝜖B }.
Element of set A∩B is "an element of set A and set B"
Example.1:
A={1, 2, 3, 4, 5, 6} and B={2, 3, 5, 7, 11}
we have to write Intersection set of A and B with common elements from set A and set B.
Here "2" is an element present in two sets and elements "3 and 5" are also present in two sets.
So these three elements are belongs to "Intersection set of A and B"
∴ A∩B = { 2, 3, 5 }
Example.2:
P={0, 2, 4, 5} and Q={1, 3, 5, 7, 9}
Here "5" is only one element present in two sets. So "5" only belongs to Intersection set of P and Q.
∴ P∩Q = { 5 }
Example.3:
A={1, 2, 3, 6} and B={0, 3, 5, 6}
∴ A∩B = { 3, 6 }
(Here "3 and 6 " are elements in common for two sets A and B)
Example.4:
A={1, 2, 3, 4, 5} and B={ }
Here set B is an Empty set(Null set) and "No element" is common for two sets. So Intersection set is also an Empty set.
∴ A∩B = { } = ϕ
Here set A and set B are called "Disjoint sets"
Disjoint sets
Two sets without common elements are called "Disjoint sets"
or
If A∩B = ϕ then set A and set B are called "Disjoint sets"
Examples:
1. A={1, 2, 3, 4} and B={ 5, 6, 7, 8 } are disjoint sets.
2. A={ a, b, c, d } and B={ x, y, z } are disjoint sets.
Note:
1. A∩B = B∩A
2. A∩Ø = Ø∩A = Ø
3. A∩A = A
4. A∩B is sub set to set A and set B ( A∩B ⊂ A, A∩B ⊂ B )
5. set A is superset to A∩B.
6. set B is superset to A∩B.
7. If A ⊂ B, then A∩B = B∩A = A
8. If B ⊂ A, then A∩B = B∩A = B