**Writing the Elements of Given Sets From Venn Diagram :**

Here we are going to see some problems based on writing elements of given sets from venn diagram.

**Question 1 :**

Using the adjacent Venn diagram, find the following sets:

(i) A - B (ii) B - C (iii) A' U B' (iv) A' n B' (v) (B U C)'

(vi) A − (B U C) (vii) A − (B n C)

**Solution :**

**(i) A - B = {4, 6, 3}**

**(ii) B - C = {-1, 5, 7}**

**(iii) A' U B'**

**A' = {-3, 0, 1, 2, 5, 7, 8}**

**B' = {-3, 0, 1, 2, 3, 4, 6}**

**A' U B' = {-3, 0, 1, 2, 3, 4, 5, 6, 7, 8}**

**(iv) A' n B'**

**A' n B' = {-3, 0, 1, 2}**

(v) (B U C)'

B U C = {-3, -,2, -1, 0, 3, 5, 7, 8}

(B U C)' = {4, 6, 1, 2}

(vi) A − (B U C)

A = {-2, -1, 3, 4, 6} and B U C = {-3, -,2, -1, 0, 3, 5, 7, 8}

A − (B U C) = {4, 6}

(vii) A − (B n C)

B n C = {-2, 8}

A = {-2, -1, 3, 4, 6}

A − (B n C) = {-1, 3, 4, 6}

**Question 2 :**

If K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h}, then find the following :

(i) K U (L n M) (ii) K n (L U M) (iii) (K U L) n (K U M)

(iv) (K n L) U (K n M) and verify distributive laws.

**Solution :**

**(i) K U (L n M)**

**(L n M) = { b, c, d }**

**K U (L n M) = {a, b, c, d, e, f}**

**(ii) K n (L U M)**

**(L U M) = {a, **b, c, d, g, h}

**K n (L U M) = {a, b, d}**

**(iii) (K U L) n (K U M)**

**(K U L) = {a, b, c, d, e, f, g}**

**(K U M) = {a, b, c , d, e, f, h}**

**(K U L) n (K U M) = {a, b , c, d , e, f}**

**(iv) (K n L) U (K n M)**

**K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h}**

**(K n L) = {b, d}**

**(K n M) = {a, b, d}**

**(K n L) U (K n M) = {a, b, d}**

After having gone through the stuff given above, we hope that the students would have understood, "Writing the Elements of Given Sets From Venn Diagram".

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