VENN DIAGRAM OF A UNION B

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

To draw venn diagram for A U B, we have to shade all the regions of A and B.

A U B

Let A and B be two sets.

Now, we can define the following new set.

A U B  =  {z | z ∈ A or z ∈ B }

(That is, z may be in A or in B or in both A and B) 

A U B is read as "A union B"

Now that A U B contains all the elements of A and all the elements of B and the figure given above illustrates this. 

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 variables inside the circle A are known as elements of the set A.

A = { a, b, d, e, g, h }

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

B = { b, c, e, f, i, j, h } 

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

A U B = { a, b, c, d, e, f, g, h, i, j } 

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

A n B = { b, e, h } 

To verify the given statement, we have to find the cardinal number of each set.

n (A)  =  6

n (B)  =  7

n (A U B)  =  10

n (A n B)  =  3

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

10  =  6 + 7 - 3

10  =  13 - 3

10  =  10

Hence it is proved.

Example 2 :

If n(U) = 38, n(A) = 16, n (AnB) = 12, n(B') = 20 find n(AUB) .

Solution :

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

n (B) = n (U) - n (B')

n (B) = 38 - 20  ==> 18

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

n (A U B) = 16 + 18 - 12

=  34 - 12

=  22

Hence the value of n (A U B) is 22.

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