# INTERSECTION OF SETS

Intersection is one of the important operations on sets which can be used to combine two or more sets to form another set.

Let us discuss this operation in detail.

Let X and Y be two sets.

Now, we can define the following new set.

X n Y = {z | z ∈ X and z ∈ Y}

(That is z must be in  both X and Y)

X n Y is read as "X intersection Y"

Now that X n Y contains only those elements which belong to both X and Y and the figure given below illustrates this. It is trivial that that X n Y ⊆ X and also X n Y ⊆ Y.

Example 1 :

Let A = {1, 3, 5, 6} and B = {0, 5, 6, 7}, find A n B.

Solution :

A n B = {1, 3, 5, 6} u {0, 5, 6, 7}

A u B = {5, 6}

Example 2 :

Let A = {-1, 0, 2, 3, 4}, B = {0, 3, 4, 5} and C = {0, 4, 5, 7}. Find (A u B) n (B u C).

Solution :

A u B = {-1, 0, 2, 3, 4} u {0, 3, 4, 5}

A n B = {-1, 0, 2, 3, 4, 5}

B u C = {0, 3, 4, 5} u {0, 4, 5, 7}

B n C = {0, 3, 4, 5, 7}

(A u B) n (B u C) = {-1, 0, 2, 3, 4, 5} n {0, 3, 4, 5, 7}

{0, 3, 4, 5}

## Related Pages

1. Union of sets

3. Symmetric difference of two sets

4. Complement of a set

5. Disjoint sets

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