1. Find the union of each of the following pairs of sets

(i) X = {1, 3, 5}        Y = {1, 2, 3}

X⋃Y = {1, 2, 3, 5}

(ii) A = {a, e, i, o, u},         B = {a, b, c}

A⋃B = {a, b, c, e, i, o, u}

(iii) A = {x:x is a natural no. and multiple of 3}

B = {x:x is a natural no. less than 6}

A⋃B = {1, 2, 3, 4, 5, 6, 9, 12, 15, ……}.

(iv) A = {x:x is a natural no. and 1 < x ≤ 6},

B = {x:x is a natural no. and 6 < x < 10}.

A⋃B = {2, 3, 4, 5, 6, 7, 8, 9}

(v) A = {1, 2, 3},      B = ɸ

A⋃B = {1, 2, 3}

2. Let A = {a, b} and B = {a, b, c}. Its ACB? What is A⋃B?

Yes, ACB

A⋃B = {a, b, c}

3. If A and B are two sets such that ACB, then what is A⋃B?

Every element of set A is contained in the set B

∴ A⋃B = B

4. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}, then find:

(i) A⋃B = {1, 2, 3, 4, 5, 6}.

(ii) A⋃C = {1, 2, 3, 4, 5, 6, 7, 8}.

(iii) B⋃C = {3, 4, 5, 6, 7, 8}

(iv) B⋃D = {3, 4, 5, 6, 7, 8, 9, 10}

(v) A⋃B⋃C = {1, 2, 3, 4, 5, 6, 7, 8}

(vi) A⋃B⋃D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(vii) B⋃C⋃D = {3, 4, 5, 6, 7, 8, 9, 10}

5. Find the intersection of each pairs of sets of the following:

(i) X = {1, 3, 5},                   (ii) Y = {1, 2, 3}

X∩Y = (1, 3}.

(ii) A = {a, e, i, o, u},           B = (a, b, c}

A∩B = (a}.

(iii) A = (x : x is a natural no. and multiple of 3}.

B = {x : x is a natural no. less than 6}.

A∩B = (3}.

(iv) A = {x : x is a natural no. and 1 < x ≤ 6},

B = {x : x is a natural no. and 6 < x < 10}.

A∩B = φ.

(v) A = {1, 2, 3}, B = φ

A∩B = φ.

6. If A = {3, 5, 7, 9, 11} and B = {7, 9, 11, 13}, C = {11, 13, 15}, D = {15, 17} then find:

(i) A∩B = {7, 9, 11}.

(ii) B∩C = {11, 13}.

(iii) A∩C∩D = φ.

(iv) A∩C = {11}

(v) B∩D = φ.

(vi) A∩ (B⋃C) = {7, 9, 11}

(vii) A∩D = φ.

(viii) A∩ (B⋃D) = {7, 9, 11}

(ix) (A∩B) ∩ (B⋃C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}

(x) (A⋃D) ∩ (B⋃C) = {3, 5, 7, 9, 15, 17} ∩ {7, 9, 11, 13, 15} = {7, 9, 11, 15}.

7.  Let A = {x : x is a natural no}, B = {x : x is an even natural no}, C = (x : x is an odd natural no}, D = (x : x is a prime no} Find:

A = (1, 2, 3, 4, 5, 6, ……}.

B = {2, 4, 6, 8, 10, 12, …….}.

C = {1, 3, 5, 7, 9, 11, …….}.

D = {2, 3, 5, 7, 9, …….}.

(i) (A∩B) =       Intersection = B ⟹ {2, 4, 6} = B

(ii) (A∩C) = Intersection = C ⟹ {1, 3, 5} = C

(iii) (A∩D) = Intersection = D ⟹ {1, 3, 5} = D

(iv) (B∩C) = Intersection = φ ⟹ φ

(v) (B∩D) = Intersection = {2}

(vi) (C∩D) = Intersection = {x : x is an odd prime no}.

8. Which of the following pairs of sets are disjoint.

(i) {1, 2, 3, 4} and {x : x is a natural no. and 4 ≤ x ≤ 6}

A = {1, 2, 3, 4},           B = {4, 5, 6}           ⟹       A∩B = {4}

So, the pair of sets are not disjoint.

(i) (a, e, i, o, u) and {c, d, e, f}

A = {a, e, i, o, u},    B = c, d, e, f}           ⟹       A∩B = {e}.