What is A Intersection B?
(A ∩ B) read as A intersection B represents that both set A and B occur at the same time. A intersection B represents the common region or common elements between two sets.
When we say A ∩ B, we’re referring to the set where both A and B occur. In simple terms, it’s all the things that are in both A and B at the same time.
Property of (A∩B)
A intersection B follows the commutative law. Hence, the commutative law for A intersection B is given as
(A∩B) = (B∩A)
A Intersection B Formula
Let’s say we have two sets, A and B, within a universal set U. Then the formula for number of elements in A intersection B is given as below:
n(A∩B) = n(A) + n(B) – n(A U B)
Where,
- n(A): This is the number of elements that belong to set A, and
- n(B): This is the number of elements that belong to set B, and
- n(A U B): This is the number of elements in total of set A and B.
It’s essentially saying that you can find the size of the intersection by adding the sizes of A and B and then subtracting the size of their union (A U B).
A Intersection B Venn Diagram
We know that A intersection B is the common region between two sets A and B. This common region between set A and Set B is represented using Venn Diagram added below:
A∩B Formula
A Intersection B Formula is an important mathematical formula used to find the common region between two sets A and B. A intersection B formula in mathematical notation is represented with the Intersection Symbol “∩” i.e., A∩B. The Intersection symbol when used with different sets is used to denote the intersection of those selected sets. This can be represented as (A ∩ B) represents that both set A and set B occur at the same time. In other words, (A ∩ B) represents elements from both set A and set B.
In this article, we will learn A intersection B Formula including the Venn diagram for A intersection B and the intersection of three sets A, B, and C in detail to understand the concept better along with some solved examples and practice problems.
Table of Content
- What is A Intersection B?
- Probability of A Intersection B
- A Intersection B Intersection C
- A Intersection B Union C
- Solved Examples on A intersection B