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.

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.

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).