A Intersection B Union C
A intersection B union C is represented as A n B U C. A intersection B union C. The set A n B U C can be obtained by taking the intersection of set A and the set B U C, and hence we can write A n B U C = A n (B U C).
Let us learn more about A intersection B union C, and how to solve it, with the help of examples, FAQs.
1.  What Is A Intersection B Union C? 
2.  How To Find A Intersection B Union C? 
3.  Examples On A Intersection B Union C 
4.  Practice Questions 
5.  FAQs On A Intersection B Union C 
What Is A Intersection B Union C?
A intersection B union C gives the elements which are in the set A and are common in both the sets, the set B and set C. The notation of A intersection B union C is A n ( B U C). Here A n ( B U C) can be computed in two simple steps. First, we need to find the union of B and C, which is B U C. Second we need to take the intersection of the set A and set B U C. Thus we can obtain A n ( B U C) in two simple steps.
The below Venn diagram shows A n ( B U C) which is the region in the set A and is common to both the sets B and set C. This A intersection B union C is identified with the shaded region in the middle of the venn diagram.
Here let us try to understand this with the help of a simple example. Let us take the set A = { 1, 2, 3, 4, 5}, B = }, B = {3, 4, 5, 6, 7}, C = {6, 7, 8, 9, 10}
B U C = {3, 4, 5, 6, 7, 8, 9, 10}
A n ( B U C) = {1, 2, 3, 4, 5} n {3, 4, 5, 6, 7, 8, 9, 10}
= {3, 4, 5}
Here we have used the basic definition that the intersection of two sets is obtained by taking the common elements and the union of two sets has been obtained by taking all the elements of the two sets. Thus we have obtained the result set A intersection B union C.
How To Find A Intersection B Union C?
The final answer of A intersection B union C can be computed from the following sequence of steps.
 First, we need to find the union of the elements of set B and set C. The is represented as B U C.
 Second, we need the intersection of the elements of set A and the resultant set B U C. This is represented as A n (B U C).
Here we have found A n ( B U C), which is the result of two simple steps of finding the union and then finding the intersection of the sets. This can be easily represented as A n B U C = A n (B U C).
āRelated Topics
 Union of Sets
 Intersection of Set
 Complement of a Set
 Difference of Sets
 A Intersection B Complement
Examples on A Intersection B Union C

Example 1: Find the set A intersection B union C, given that A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7}, and C = {3, 4, 5, 6, 7, 8, 9}.
Solution:
The given sets are as follows.
A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7}, and C = {3, 4, 5, 6, 7, 8, 9}
The aim is to find A intersection B union C.
A n B U C = A n ( B U C)
= {1, 2, 3, 4, 5} n ({4, 5, 6, 7} U {3, 4, 5, 6, 7, 8, 9})
= {1, 2, 3, 4, 5} n {3, 4, 5, 6, 7, 8, 9}
= {3, 4, 5}
Therefore, the set A intersection B union C is {3, 4, 5}.

Example 2: Find the set A intersection B union C, given that A = {4, 5}, B U C = { 2, 3, 4, 5, 6, 7}.
Solution:
The given sets are as follows.
A = {4, 5}, B U C = { 2, 3, 4, 5, 6, 7}.
The aim is to find A intersection B union C.
A n (B U C) = {4, 5} n { 2, 3, 4, 5, 6, 7}
= {4, 5}
Therefore, A n (B U C) is equal to {4, 5}.
FAQs on A Intersection B Union C
What Is A Intersection B Union C?
A intersection B union C is represented as A n B U C. This is obtained by taking the common elements of the set A and the set B U C, which can be represented as A n B U C = A n ( B U C).
How To Find A Intersection B Union C?
The set A intersection B union C can be found in two simple steps. First, we need to find the set of B U C. As a second step we need to find the intersection of the set A and the set B U C to obtain A n ( B U C).
What Is The Formula Of A Intersection B Union C?
The formula of A intersection B union C is A n B U C. It is the intersection of two sets, the set A and the set B U C. Thus we have the formula A n B U C = A n ( B U C).
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