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 number and multiple of 3}, B = {x : x is a natural number less than 6}
A={3,6,9,12,...}, B={1,2,3,4,5}
A∪B={1,2,3,4,5,6,9,12,...}

(iv) A = {x : x is a natural number and 1 < x ≤6 }, B = {x : x is a natural number and 6 < x < 10 }
A={2,3,4,5,6}, B={7,8,9}
A∪B={2,3,4,5,6,7,8,9}

(v) A = {1, 2, 3}, B = φ
A∪B=A∪ϕ=A={1,2,3}
 
2. Let A = { a, b }, B = {a, b, c}. Is A ⊂ B ? What is A ∪ B ?
Yes, A⊂B.
A∪B={a,b,c}

3. If A and B are two sets such that A ⊂ B, then what is A ∪ B ?
If A⊂B, then 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 }; 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 pair of sets.
(i) X = {1, 3, 5} 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 number and multiple of 3}, B = {x : x is a natural number less than 6}
A={3,6,9,12,...}, B={1,2,3,4,5}
A∩B={3}

(iv) A = {x : x is a natural number and 1 < x ≤6 }, B = {x : x is a natural number and 6 < x < 10 }
A={2,3,4,5,6}, B={7,8,9}
A∩B=ϕ

(v) A = {1, 2, 3}, B = φ
A∩B=A∩ϕ=ϕ

6. If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}and D = {15, 17}; 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) = {3,5,7,9,11,15,17}∩{7,9,11,13,15}={7,9,11,15}

7. If A = {x : x is a natural number }, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number }, find
(i) A ∩ B (ii) A ∩ C (iii) A ∩ D (iv) B ∩ C (v) B ∩ D (vi) C ∩ D
A={1,2,3,4,...}, B={2,4,6,8,...}, C= {1,3,5,7,9,...}, D= {2,3,5,7,11,13,17,..}
(i) A ∩ B = {2,4,6,8,...} = B
(ii) A ∩ C = {1,3,5,7,...} = C
(iii) A ∩ D = {2,3,5,7,...} = D
(iv) B ∩ C = ϕ
(v) B ∩ D = {2}
(vi) C ∩ D = {3,5,7,11,13,...} = {x: x is an odd prime number}

 8. Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }
{1,2,3,4} ∩ {4,5,6} = {4}
∴ this pair of sets is not disjoint.

(ii) { a, e, i, o, u } and { c, d, e, f }
{a,e,i,o,u} ∩ {c,d,e,f} = {e}
∴ this pair of sets is not disjoint.

(iii) {x : x is an even integer } and {x : x is an odd integer}
{2,4,6,8,...} ∩ {1,3,5,7,...} = ϕ
∴ this pair of sets is disjoint.

9. If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5,10, 15, 20 }; find
(i) A – B = {3,6,9,15,18,21}
(ii) A – C = {3,9,15,18,21}
(iii) A – D = {3,6,9,12,18,21}
(iv) B – A = {4,8,16,20}
(v) C – A  = {2,4,8,10,14,16}
(vi) D – A = {5,10,20}
(vii) B – C = {20}
(viii) B – D = {4,8,12,16}
(ix) C – B = {2,6,10,14}
(x) D – B = {5,10,15}
(xi) C – D = {2,4,6,8,12,14,16}
(xii) D – C = {5,15,20}

 10. If X= { a, b, c, d } and Y = { f, b, d, g}, find
(i) X – Y = {a,c}
(ii) Y – X = {f,,g}
(iii) X ∩ Y = {b,d}

11. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
R − Q is a set of irrational numbers.

12. State whether each of the following statement is true or false. Justify your answer.
(i) { 2, 3, 4, 5 } and { 3, 6} are disjoint sets. 
False
∵ {2,3,4,5}∩{3,6}= {3}

(ii) { a, e, i, o, u } and { a, b, c, d }are disjoint sets.
False
∵ {a,e,i,o,u}∩{a,b,c,d} = {a}

(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.
True
∵ {2,6,10,14} ∩ {3,7,11,15} = ϕ

(iv) { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.
True
∵ {2,6,10}∩ {3,7,11} = ϕ