**Venn diagram for A complement :**

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

To draw a venn diagram for A', we have shade the region that excludes A

**A'**

To draw a venn diagram for B', we have shade the region that excludes B

**B'**

If A ⊆ U, where U is a universal set, then U \ A is called the compliment of A with respect to U. If underlying universal set is fixed, then we denote U \ A by A' and it is called compliment of A.

**A' = U \ A **

The difference set set A \ B can also be viewed as the compliment of B with respect to A.

If B ⊆ U, where U is a universal set, then U \ B is called the compliment of B with respect to U. If underlying universal set is fixed, then we denote U \ B by B' and it is called compliment of B.

**B' = U \ B **

The difference set set B \ A can also be viewed as the compliment of B with respect to A.

**Example 1 :**

From the venn diagram, write the elements of the following sets

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

**Solution :**

(i) A'

A' = { c, f, i ,j }

(ii) B'

B' = { a, d, g }

(iii) (A n B)'

(A n B)' = { a, d, g, c, f, i, j }

(iv) (A U B)'

(A U B)' = { } (or) null set

**Example 2 :**

If n(U) = 43, n (A) = 26 find n (A')

**Solution :**

By using the formula,

n (A) + n (A') = n (U)

we may find the value of n (A')

26 + n (A') = 43

Subtract 26 on both sides

26 - 26 + n (A') = 43 - 26

n (A') = 17

**Example 3 :**

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

**Solution :**

By using the formula,

n (B) + n (B') = n (U)

we may find the value of n (B')

n (B) + 20 = 38

Subtract 20 on both sides

n (B) + 20 - 20 = 38 - 20

n (B) = 18

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

= 16 + 18 - 12

= 34 - 12

= 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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