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A Intersection B Intersection C
A intersection B intersection C represents the common elements of the sets A, B, and C respectively. This is generally represented as A n B n C. The symbol 'n' represents intersection and gives the common element of the two sets. Finding the common elements of the three given sets, A intersection B intersection C, is difficult and hence we first find the common elements of two sets A, B, and B, C at a time. Here we first find A n B and B n C, and finally, we get the answer for A n B n C.
Hence we have the formula A n B n C = (A n B) n ( B n C). Let us learn more about A intersection B intersection C, and how to find A intersection B intersection C, with the help of examples, FAQs.
What Is A Intersection B Intersection C?
A intersection B intersection C, as a set, gives the elements which are common to all the sets A, B, C. The notation of A intersection B intersection C can be represented as A n B n C. This can also be found in two steps. First, the common elements of sets A and B, or A n B can be identified, and then the common elements of sets B and C, or B n C can be identified, and then the common elements of these two results can be computed to find A intersection B intersection C. The elements of the resultant set of A intersection B Intersection C are the elements that are common to set A, set B, and set C.
The below venn diagram shows that the common elements of A, B and C or the overlapping common region of these three circles represent the set A n B n C.
The result of A intersection B intersection C can be understood with the help of a simple example. Let us take the three sets as A = {a, b, c, d, e}, B = {c, d, e, f, g}, and set C = {d, e,f, g, h, i}. Let us now take the intersection of two sets at a time.
A n B = {c, d, e}
B n C = {d, e, f, g}
A n B n C = (A n B) n (A n C)
= {c, d, e} n {d, e,f, g}
= {d, e}
Here we have used the basic definition that the intersection of sets is obtained by taking the common elements and thus obtained the set A intersection B intersection C.
How To Find A Intersection B Intersection C?
A intersection B intersection C can be easily computed from the following sequence of steps.
 First, we need to find the intersection of the elements of set A and set B. The is represented as A n B.
 Second, we need the intersection of the elements of set B and set C. This is represented as B n C.
 The third and final step is to find the intersection of the two outcomes of intersection elements. Here we need to take the inspection of A n B and B n C. And we have the final answer of A intersection B intersection C. This can be easily represented as A n B n C = (A n B) n (B n C).
☛Related Topics
 A Intersection B Complement
 Intersection of Set
 Union of Sets
 Complement of a Set
 Difference of Sets
Examples on A Intersection B Intersection C

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

Example 2: Find the set A intersection B intersection C, given that A = {6, 7, 8, 9, 10}, and B n C = {5, 6, 7}
Solution:
The given sets are A = {6, 7, 8, 9, 10}, and B n C = {5, 6, 7}.
The aim is to find A intersection B intersection C.
A n B n C = A n (B n C)
= {6, 7, 8, 9, 10} n {5, 6, 7}
= {6, 7}
Therefore, A n B n C is equal to {6, 7}.
FAQs on A Intersection B Intersection C
What Is A intersection B intersection C?
A intersection B intersection C gives the common elements of the sets A, B, C. It is represented as A n B n C. The resultant answer of this set is contained in the individual sets, set A, set B, set C respectively.
What Is the Notation of A Intersection B Intersection C?
The set notation to represent A intersection B intersection C is A n B n C.
How To Find A Intersection B Intersection C?
The set A intersection B intersection C can be obtained in a sequence of steps. First, we need to find A n B and B n C individually. Finally, we find the intersection of the resultant of these two sets A n B and B n C to find the required set A n B n C.
What Is The Formula Of A Intersection B Intersection C?
The formula of A intersection B intersection C is represented as A n B n C, and it is equal to the intersection of the set of two sets A n B and B n C. Thus we have A n B n C = ( A n B) n ( B n C).
What Are the Different Ways of Representing A Intersection B Intersection C?
The elements of A intersection B intersection C can be represented using venn diagram, roster form, and by using set builder notation. Further venn diagram is easy to understand and is the best means to represent A intersection B intersection C.
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