**Venn diagram of a intersection b whole complement :**

Here we are going to see how to draw a venn diagram of A intersection B whole complement.

**Venn diagram of (A n B)' : **

To represent (A n B)' in venn diagram, we have to shade the region except the common regions of A and B.

**(A n B)'**

**A' U B'**

Venn diagrams for (A n B)' = A' U B'

Let us look into some examples to understand the above concepts.

**Example 1 :**

Use the Venn diagram to answer the following questions

List out the elements of the following sets

(1) U |
(2) G |
(3) H |
(4) G' |

(5) H' |
(6) G' n H' |
(7) n(GUH)' |
(8) n(GnH)' |

**Solution :**

(1) To find the elements of universal set U, we have to list out all the elements that we find in the rectangular box.

U = { 1, 2, 3, 4, 5, 6, 8, 9, 10 }

(2) To write the elements of set G, we have to list out the numbers that we find in the circle G.

G = { 1, 2, 4, 8}

(3) To write the elements of set H, we have to list out the numbers that we find in the circle H.

H = { 2, 6, 8, 10}

(4) To find the elements of the set G', we have to list out all the elements other than the circle G.

G' = { 3, 5, 6, 9, 10 }

(5) To find the elements of the set H', we have to list out all the elements other than the circle H.

H' = { 1, 3, 4, 5, 9 }

(6) G' n H' = { 3, 5, 9 }

(7) To find (G U H)', first we have to find the elements of

G U H = {1, 2, 4, 6, 8, 10}

(G U H)' = {3, 5, 9}

n (G U H)' = 3

(8) To find (G n H)', first we have to find the elements of

G n H = { 2, 8}

(G n H)' = { 1, 3, 4, 5, 6, 9, 10 }

n (G n H)' = 7

**Example 2 :**

If U = {x : 1 ≤ x ≤ 10, x ∊ N}, A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 9, 10}, find

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

**Solution :**

U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

A = {1, 3, 5, 7, 9}

B = {2, 3, 5, 9, 10}

(i) A' = { 2, 4, 6, 8, 10}

(ii) B' = { 1, 4, 6, 7, 8}

(iii) A' U B' = { 1, 2, 4, 6, 7, 8, 10 }

(iv) A' ⋂ B' = { 4, 6, 8 }

- 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

After having gone through the stuff given above, we hope that the students would have understood "Venn diagram of a intersection b whole complement".

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