Intersection of Sets
Define Intersection of Sets.
Intersection of Sets is the set of common elements in all the sets. It is denoted by symbol ∩.
What does A ∩ B?
A ∩ B mean the set of elements common to both set A and set B
Write the Set Builder form of the Intersection of Sets.
The set builder form of the intersection of sets:
P ∩ Q = {x: x ∈ P and x ∈ Q}
Where P and Q are two sets.
What are the Properties of the Intersection of Sets.
The properties of intersection of sets are:
- Commutative Law
- Associative Law
- Distributive Law
- Law of Empty set ϕ and Universal set U
- Idempotent Law
What is the formula for finding the Cardinality of the Intersection of Sets?
The formula for finding cardinality intersection of sets is given by:
n(A∩B) = n(A) + n(B) – n(A∪ B)
Where,
- n(A) is cardinality of set A
- n(B) is cardinality of set B
- n(A ∪ B) is cardinality of set A ∪ B
- n(A ∩ B) is cardinality of set A ∩ B
What does ∩ and ⋃ mean in math?
In math, ∩ mean intersection and ⋃ mean union of sets
Intersection of Sets
Intersection of Sets is the operation in set theory and is applied between two or more sets. It result in the output as all the elements which are common in all the sets under consideration. For example, The intersection of sets A and B is the set of all elements which are common to both A and B.
Intersection of Sets
In other words, it is an operation that selects the common identical element among the sets. For example
Suppose, Set A is the set of odd Numbers less than 10 and Set B is the set of first 5 multiple of 3.
⇒ A = {1,3,5, 7,9}
⇒ B = {3,6,9,12,15}
So the common element in these two set are 3 and 9.
Hence, the set of intersection of A and B = {3,9}