VENN DIAGRAM FOR a INTERSECTION B

Here we are going to see how to draw a venn diagram for A intersection B.

To draw a venn diagram for A n B, we have to shade the common region that we find in both circles.

A n B

Let A and B be two sets.

Now, we can define the following new set.

A n B  =  {z | z ∈ A and z ∈ B}

(That is z must be in  both A and B)

A n B is read as "A intersection B"

Now that A n B contains only those elements which belong to both A and B and the figure given above illustrates this. 

It is trivial that that A n B ⊆ A and also A n B ⊆ B 

Example 1 :

From the given Venn diagram find

(i) A (ii) B (iii) A U B (iv) A n B

Also verify that n(A U B) = n(A) + n(B) - n(A n B)

Solution :

The numbers inside the circle A are known as elements of set A.

A = { 2, 3, 4, 5, 6, 7, 8, 9 }

n (A)  =  8

The numbers inside the circle B are known as elements of set B.

B = { 3, 6, 9 }

n (B) = 3

The numbers inside the circles A and B are known as elements of the set AUB.

A U B = { 2, 3, 4, 5, 6, 7, 8, 9 }

n (A U B) = 8

The numbers in common region of A and B is known as elements of A n B.

A n B = {3, 6, 9}

n (A n B) = 3

n(A U B) = n(A) + n(B) - n(A n B)

8 = 8 + 3 - 3

8 = 8

Hence it is proved.

Example 2 :

From the venn diagram, write the elements of set A n B

Solution :

The variables in common region of A and B are known as elements of A n B.

A n B = { b, e, h } 

Example 3 :

If n(A) = 12, n(B) = 17 and n(A U B) = 21, find n(A n B)

Solution :

By using the formula,

n(A U B) = n (A) + n (B) - n (A n B)

we may find the value of n (A n B)

21  =  12 + 17 - n (A n B)

21  =  29 - n (A n B)

n (A n B)  =  29 - 21  ==>   8

Hence the value of n (A n B) is 8. 

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