Set One
Practice the questions provided in the worksheet on difference of two sets. The questions
are based on finding the differences between the two given sets.
1. If set A = {3, 4, 5, 6} and set B = {2, 4, 6, 8};
Find:
(i) A –B
(ii) B - A
2. Given set A = {2, 4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15, 18} and set C = {0, 6, 12, 18};
Find:
(i) A – B
(ii) B – C
(iii) C – A
(iv) A - C
3. Given: P = {a, c, d , m}, Q = {c, e, m, x} and R = {a, e, i, o};
Find:
(i) P – R
(ii) Q – P
(iii) R - Q
4. If A = {Counting numbers between 30 and 40},
B = {Counting numbers between 20 and 50 which are divisible by 4}.
Find:
(i) A – B
(ii) B - A
5. If P = {letters in the word ‘BANARAS’}
Q = {Letters in the word ‘BHARAT’}
and R = {letters in the word ‘BHATINDA’};
Find:
(i) P – Q
(ii) R – Q
(iii) P - R
6. If M = {2, 4, 6, 8, 10, 12} and N = {3, 4, 5, 6, 7, 8, 10}.
Find:
(i) M – N
(ii) N – M
(iii) (M - N) ∪ (N - M)
Set two
Practice the set of questions provided in the worksheet on set operations. The questions
are based on finding the union and intersections of the given sets.
1. Write down the union and intersection of the following pairs of sets:
(i) A = {1, 2, 3, 4, 5, 6}
B = {1, 3, 5, 7, 9}
(ii) X = {a, b, c, d, e}
Y = {c, e, f, g}
(iii) P = {x : x is a multiple of 2 between 9 and 21}
Q = {x : x is a multiple of 3 between 10 and 20}
(iv) M = {letters in the word ‘COMPUTER’}
N = {letters in the word ‘CALCULATOR’}
2. Let A = set of natural numbers less than 8,
B = {even natural numbers less than 12}
C = {Multiples of 3 between 5 and 15}
and D = {Multiples of 4 greater than 6 and less than 20};
Find:
(i) B ∪ C
(ii) A ∪ D
(iii) C ∪ D
(iv) A ∩ C
(v) (B ∩ C) ∪ A
(v) (D ∪ A) ∩ B
(vii) (A ∩ C) ∪ (B ∩ D)
(viii) (B ∪ D) ∩ (C ∪ A)
SET THREE
Worksheet on empty sets will help us to practice different types of questions to state
whether the sets are empty or not. We know, the set which contains no element is called
an empty set. It is also known as null set or void set.
1. Which of the following sets are empty?
(i) Set of counting numbers between 5
(v) {0}
and 6.
(vi) { }
(ii) Set of odd numbers between 7 and 19.
(vii) {Prime numbers between 7 and 11}
(iii) Set of odd numbers between 7 and 9.
(viii) {x | x ∈ N and 3< x < 4}
(iv) Set of even numbers which are not
divisible by 2.
2. State, whether or not the following sets are empty:
(i) {1, 4, 7, 10, ………, 31}
(iii) {x | x22 = 0}
(ii) {Month having more than 31 days}
(iv) {x | x ∈ N and x < 1}
(v) {Prime numbers divisible by 2}
(xi) {People who are 500 years old}
(vi) {Negative natural numbers}
(xii) {Prime numbers between 17 and 23}
(vii) {Women who are 5 meter tall}
(xiii) {Set of even numbers, not divisible
(viii) {Men with four legs}
by 2}
(ix) {Integers less than 5}
(xiv) {Set of multiples of 3, which are
(x) {A week having 10 days}
more than 9 and less than 15}
SET FOUR
Practice the set of questions provided in the worksheet on representation on set. The
questions are based on representing the set using both the methods Roster Form and SetBuilder Form.
Write each of the following sets in Roster (tabular) Form and also in Set-Builder
Form:
(i) Set of all natural numbers which can divide 24 completely.
(ii) Set of odd numbers between 20 and 35.
(iii) Set of even natural numbers less than 25.
(iv) Set of letters used in the word ‘MASSACHUSETTS’.
(v) Set of names of the first five months of a year.
(vi) Set of all two digit numbers which are perfect square also.
(vii) Set of letters used in the word ‘EDUCATION’.
Set of natural numbers divisible by 7
Roster Form: {7, 14, 21, 28, 35, 42, 49, …….}
Set-Builder Form: {x : x is a natural number divisible by 7}
OPERATIONS OF SET
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
(f) P ∪ Q ∪ S
(k) Q ∩ S
(b) P ∪ R
(g) Q ∪ R ∪ S
(l) P ∩ Q ∩ R
(c) Q ∪ R
(h) P ∩ Q
(m) P ∩ Q ∩ S
(d) Q ∪ S
(i) P ∩ R
(n) Q ∩ R ∩ S
(e) P ∪ Q ∪ R
(j) Q ∩ R
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
(c) C - D
(e) B - A
(g) D - C
(b) B - C
(d) D - A
(f) C - B
(h) A - D
5. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is universal set
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}
(d) {x : x ≥ 10}
(b) {x : x is a multiple of 2}
(e) {x : x Є N, 5x + 1 > 20}
(c) {x : x is a perfect cube}
(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 = { }
(c) D = {a, b, c, d, e, f}
(e) E = {b, c}
(b) B = {c, d, f}
(d) C = {a, b, d}
(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')
In worksheet on Venn Diagrams we will solve 8 different types of questions on sets, to
draw Venn Diagrams in different situations.
1. What set is represented by the shaded portion in the following Venn diagrams?