**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.

- Venn diagram A U B
- Venn diagram A n B
- Venn diagram of A'
- Venn diagram of B'
- Venn diagram of (AUB)'
- Venn diagram of (AnB)'
- Venn diagram of A\B
- Venn diagram of B\A

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