INTERSECTION OF SETS

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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}

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