Worksheet on operation on sets we will solve 10 different types questions on math sets.
1. Find the union of each of the following pairs of sets.
(a) A = {2, 4, 6}
B = {1, 2, 3}
(b) P = {a, e, i, o, u}
Q = {a, b, c, d}
(c) X = {x : n ∈ N, x = 2n, n < 4}
Y = {x : x is an even number less than 10}
(d) M = {x : x is natural number and multiple of 3}
N = {x : x is a prime number less than 19}
(e) D = {x : x is an integer -3 < x < 3}
E = {x : x is a factor of 8}
(f) G = {x : x ∈ N, x < 7}
H = {x : x ∈ Z, -2 ≤ x ≤ 3}
2. Find the intersection of each of the following pairs of sets.
(a) A = {1, 4, 9, 16}
B = {3, 6, 9, 12}
(b) C = {p, q, r, s}
D = {a, b}
(c) P = {x : n ∈ N, x = 3n n< 3}
Q = {x : x ∈ N x < 7}
(d) X = {x : x is a letter of the word ‘LOYAL’}
Y = {x : x is a letter in the word ‘FLOW’}
(e) G = {x : x = n2, when n ∈ N}
H = {x : x = 4n, when n ∈ W n < 5}
3. If P = {1, 2, 3} Q = {2, 3, 4} R = {3, 4, 5} S = {4, 5, 6}, find
(a) P ∪ Q
(b) P ∪ R
(c) Q ∪ R
(d) Q ∪ S
(e) P ∪ Q ∪ R
(f) P ∪ Q ∪ S
(g) Q ∪ R ∪ S
(h) P ∩ Q
(i) P ∩ R
(j) Q ∩ R
(k) Q ∩ S
(l) P ∩ Q ∩ R
(m) P ∩ Q ∩ S
(n) Q ∩ R ∩ S
4. If A = {a, b, c, d} B = {b, c, d, e} C = {c, d, e, f} D = {d, e, f, g}, find
(a) A - B
(b) B - C
(c) C - D
(d) D - A
(e) B - A
(f) C - B
(g) D - C
(h) A - D
5. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 4, 6, 8, 10}
B = {1, 3, 5, 7, 8, 9}
Find:
(a) A'
(b) B'
(c) A' ∪ B'
(d) A' ∩ B'
(e) (A ∪ B)'
Also show (A ∪ B)' = A' ∩ B'.
6. Find the complement of the following sets if universal set is the set of natural numbers.
(a) {x : x is a prime number}
(b) {x : x is a multiple of 2}
(c) {x : x is a perfect cube}
(d) {x : x ≥ 10}
(e) {x : x Є N, 5x + 1 > 20}
(f) {x : x is an odd natural number}
Worksheet on Operation on Sets
7. If U = {a, b, c, d, e, f} find the complement of the following.
(a) A = { }
(b) B = {c, d, f}
(c) D = {a, b, c, d, e, f}
(d) C = {a, b, d}
(e) E = {b, c}
(f) F = {a, c, f}
8. If U = {1, 2, 3, 4, 5, 6} and A = {2, 3, 6}, find
(a) A ∪ A'
(b) ∅ ∩ A
(c) A ∩ A'
(d) U' ∩ A
9. Let P = {1, 3, 5, 7} Q = {3, 7, 9, 11} R = {1, 5, 8, 11}, then verify the following.
(a) P ∪ Q = Q ∪ P
(b) (P ∪ Q) ∪ R = P ∪ (Q ∪ R)
(c) P ∩ Q = Q ∩ P
(d) (P ∩ Q) ∩ R = P ∩ (Q ∩ R)
(e) P ∪ (Q ∩ R) = (P ∪ Q) ∩ (P ∪ R)
(f) P ∩ (Q ∪ R) = (P ∩ Q) ∪ (P ∩ R)
Worksheet on Operation on Sets
10. Let U = {a, b, c, d, e, f, g}, A = {a, c ,f , g}, B = {f, g, b, d}
Verify:
(a) (A ∪ B)' = (A' ∩ B')
(b) (A ∩ B)' = (A' ∪ B')
Answers for worksheet on operation on sets are given below so that students can check the answers.
Worksheet on Operation on Sets Answers:
1. (a) {1, 2, 3, 4, 6}
(b) {a, b, c, d, e, i, o, u}
(c) {2, 4, 6, 8}
(d) {2, 3, 5, 7, 9, 11, 13, 17, 6, 9, 12, 15, ….}
(e) {-2, -1, 0, 1, 2, 4, 8}
(f) {-2, -1, 0, 1, 2, 3, 4, 5, 6}
2. (a) {9}
(b) d
(c) {3, 6}
(d) {L, O}(e) {4, 16}
3. (a) {1, 2, 3, 4}
(b) {1, 2, 3, 4, 5}
(c) {2, 3, 4, 5}
(d) {2, 3, 4, 5, 6}
(e) {1, 2, 3, 4, 5}
(1) {1, 2, 3, 4, 5, 6}
(g) {2, 3, 4, 5, 6}
(h) {2, 3}
(i) {3}
(j) {3, 4}
(k) {4}
(l) {3}
(m) ∅
(n) {4}
4. (a) {a}
(b) {b}
(c) {c}
(d) {e, f, g}
(e) {e}
(f) {f }
(g) {g}
(h) {a, b, c}
5. {3, 5, 7, 9}
(b) {2, 4, 6, 10}
(c) {2, 3, 4, 5, 6, 7, 9, 10}
(d) {∅}
6. (a) {x : x is composite number and 1}
(b) {x : x is odd}
(c) {x : x is not a perfect cube}
(d) {x : x < 10, x ∈ N}
(e) {x : x ∈ N and x < 4}
(f) {x : x is even}
7. (a) U
(b) {a, b, e}
(c) ∅
(d) {c, e, f}
(e) {a, d, e, f}
(f) {b, d, e}
8. (a) U
(b) A
(c) ∅
(d) ∅
Worksheet on Operation on Sets
● Sets and Venn-diagrams Worksheets
● Worksheet on Elements Form a Set
● Worksheet to Find the Elements of Sets
● Worksheet on Properties of a Set
● Worksheet on Sets in Roster Form
● Worksheet on Sets in Set-builder Form
● Worksheet on Finite and Infinite Sets
● Worksheet on Equal Sets and Equivalent Sets
● Worksheet on Union and Intersection of Sets
● Worksheet on Disjoint Sets and Overlapping Sets
● Worksheet on Difference of Two Sets
● Worksheet on Operation on Sets
● Worksheet on Cardinal Number of a Set
Math Home Work Sheets
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