**Sets Class 7
ICSE Worksheets**

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**Sets Class 7
ICSE Worksheet 1**

**1. **State whether each of the following pairs of sets are equivalent,
equal or overlapping sets.

a.
*A = *{*x: x Ñ” ***Z** , 2 ≤ x ≤ 2} and B = {*x *: *x *is
the letter of the word PLATE}

b.
C = {*x *: *x *Ñ” **N **and *x *is a multiple of 3} and D = {*x
*: *x *Ñ” **N **and *x *is a multiple of 2}

c.
A = {1, 2, 3, 4} and B = {2, 3, 5, 7, 11}

d.
E = {*x *: *x *is a letter of the word WHITE} and F = {e, t, h, w, i}

e.
A *= *{*x *| *x *is a multiple of 2 less than 10} and B = {2, 4,
6, 8}

f. A = {p, o, c,
k, e, t} and B = {l, o, c, k, e, t}

**2.
**Fill in the blanks.

a.
A = {*x *: *x *is a letter of the word ASSASSINATION} written in
roster form is ___________.

b.
B = {the letters of the word CARROT} and C = {the letters of the word COAT} are
two ___________ sets.

c.
If A = {5, 10, 15, 20, 25} and B = {5, 15, 25}, B is a ___________ of A.

d.
If E = {*x *: *x *is a letter of the word INDIA}, F = {*x *: *x
*is a letter of the word DIANA}, then E and F are two ___________ sets.

e. If G = {*x *:
*x *is a prime number and *x *< 1}, then G is a/an ___________ set.

**3.** State whether the following statements are true or false.

a.
A set and the complement of a set are two overlapping sets.

b.
A = {x: −5 < x < −2, x Ñ” **Z**}, then *n*(A) = 6.

c.
A = {triangles}, B = {scalene triangles}, then B ⊆ A.

d.
If A and B are two sets such that A is a subset of B and A ≠ B, then A is said
to be a proper subset of B*.*

**4.
**Let P = set of all triangles, Q = set of
scalene triangles, R = set of isosceles triangles, S = set of equilateral
triangles. State which of the following are true.

a. S ⊆ R b. Q ⊆ P

c. P ⊆ S d. R ⊆ P

e. R ⊆ Q

**5.
**Write the following sets in the roster form.

a.
A = {*x *: *x *is the letters of the word CONSTANTINOPLE}.

b.
B = {*x *: *x *= 2*n*, *n Ñ”* **N**, n ≤ 7}.

c.
C = {*x *: *x *is a prime number, 5 < *x *< 17}.

d.
D = {*x *: *x *are different types of triangles}.

e.
E = {*x *: *x *= 2*n *– 1, *n *Ñ” **W**, n ≤ 6}.

**6.
**If P = {2, 3, 4, 5}, then write down all the
subsets of P.

**7.
**Choose the correct option.

a.
P = {*x *: *x *is an even prime number} is a/an

i. infinite set

ii. singleton set

iii. finite set

iv. null set

b.
A = {2, 4, 6, 8, 10} and B = {1, 2, 3, 4, 5, 6}, then A and B are

i. overlapping sets

ii. disjoint sets

iii. equal sets

iv. equivalent sets

c.
If A = {*a*, *b*, *c*, *d*, *e*} and B = {letters of
the word BEAD}, then

i. B = A

ii. B ⊆A

iii. *n*(B) = *n*(A)

iv. disjoint set

d.
**Î¾** = {1, 2, 3, 4, 5, 6, 7, 8} and A =
{2, 4, 6, 8}, then A′ is

i. {5, 6, 7, 8}

ii. {1, 2, 3, 4}

iii. {1, 3, 5, 7}

iv. {4, 6, 7}

**8.
**If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A =
{2, 4, 6, 8, 10}, then find A′.

**9.
**Identify the following as finite, infinite,
empty or singleton set.

a. A = {1, 2, 3, 4, 5, 6}

b. B = {*x *: *x *is a
vowel in the word BOOK}

c.
C = {*x *: *x *is an even integer}

d. D = {*x *: *x *is an
even prime number greater than 2}

**Sets Class 7
ICSE Worksheet 2**

**1.
**Fill in the blanks.

a.
If A = {*x *: *x *≤ 6, *x *is an even whole number}, then A in
roster form is ___________.

b.
A is the set of the letters of the word MISSISSIPPI, then *n*(A) =
___________.

c. All equal sets are equivalent set but all equivalent sets are not ___________.

d. If Î¾ is the universal set and Q is the null set, then Q′ is equal to ___________.

**2.
**Given Î¾ = {1, 3, 4, 7, 9, 13, 14, 15, 17, 18,
27},

A
= { *x*:* x* Ñ” Î¾, x * *is
an odd number},

B
= { *x: x *Ñ” Î¾, x* *is a prime number},

C
= { *x: x *Ñ” Î¾,* x *is a multiple of 3} and

D = { *x; x *Ñ”
Î¾, *x *is a multiple of 7}

a.
List the elements of the following subsets of X.

i. A ii. B

iii. C iv. D

v. C′

vi. elements common to *A *and
*B *

vii.
elements common to B and C

b. Write down the cardinal number of each of the sets A, B, C and D.

c. Write down the pairs of overlapping sets.

**3.
**Match the following with the correct answer.

a. B = {2, 3, 5, 7, 11, 13}, C = {*a*,
*b*, *c*, *d*, *e*, *f *},

then B and C are two i. {violet, indigo, blue, green, yellow,
orange, red}

b. D = {*x *: *x *is the
measure of the angles

of an isosceles right-angled triangle}
ii. {E, X,
M, I, N, A, T, O}

c. E = {*x *: *x *is a
colour of the rainbow} iii. Equivalent sets

d. F = {*x *:
letters of the word EXAMINATION} written is roster
form is iv. {90°, 45°}

**4.
**State true or false.

a.
The collection of interesting stories in a school library forms a set.

b.
The collection of types of quadrilaterals forms a set.

c.
Equivalent sets are always equal.

d.
*n*(A) of a null set is equal to zero.

e. If U = {–2, –1, 0, 1, 2, 3} and B = {1, 2, 3}, then B′ = {–2, –1, 0}.

**5.
**Write the following sets in set builder form.

a. {2, 3, 5, 7, 11}

b. {7, 14, 21, 28, 35, 42, 49}

c. {a, e, i, o, u}

d. {p, e, n, c, i, l}

e.
{January, June, July}

**6.
**Find the number of subsets of each of the
following sets.

a. A = {10, 12, 14, 16, 18}

b. B = {*x *| *x *is
a prime number between 10 and 20}.

**7.
**List the proper subsets of set A where A = {*x *| *x
*is a letter of the word TEST}.

**8.
**Choose the correct option.

a.
A = {1, 2, 3, 4, 5} is a

i. finite set

ii. infinite set

iii. empty set

iv. singleton set

b.
Cardinal number of B = {x: x ≤ 15, x
Ñ” W} is

i. 0

ii. 15

iii. 16

iv. 14

c.
P = {*x *: *x *is a day of a week starting with the letter A} is a/an

i. singleton set

ii. finite set

iii. null set

iv. infinite set

d. If A = {*x *:
*x *is the letter of the word TEACHER} and B = {t, e, a, c, h, r}, then
the two sets are

i. equal

ii. equivalent

iii. overlapping

iv. disjoint

**9.
**If A = {x : x Ñ” W, x ≤ 12}, B = {x: x Ñ” N, 5
≤ x ≤ 20}* *and C = { *x: x *∈ **N, ***x *is a multiple of 7
≥ 14}, identify the following:

a. Disjoint sets

b. *n*(A)

c. Elements common to A and B.

**Crossword
**

**Across
**

4.
A well-defined collection of objects is known as ________.

5.
A set having uncountable number of different elements is called a ________ set.

7.
If the number of elements in a set are equal, they are said to be ________.

8.
The complement of the universal set is ________ set.

9.
A method of representing set in which all elements are listed and are separated
by commas.

10.
Two sets are said to be ________ if they have same elements.

**Down **

1. A non-empty set which does not
contain all the elements of superset is known as ________ subset.

2. Two sets are ________ if they have
no element in common.

3. A set having only one element.

6. A set which consists of all
elements of different sets under considerations called the ________ set.

**ANSWERS**

**Worksheet 1**

1. a. Equivalent
set

b. Overlapping set

c. Overlapping set

d. Equal set

e. Equal set

f. Overlapping set

2. a. A = {A, S,
I, N, T, O}

b. overlapping

c. subset

d. equal

e. empty

3. a. False b. False

c. True d. True

4. a. False b. True

c. False d. True

e. False

5. a. A = {C, O, N,
S, T, A, I, P, L, E}

b. B = {2, 4, 6, 8, 10, 12, 14}

c. C = {7, 11, 13}

d. D = {Scalene, Isosceles, Equilateral,
Acute-angles, Obtuse-angled, Right-angled}

e. E = {-1, 1, 3, 5, 7, 9, 11}

6. Subsets of P =
{}, {2}, {3}, {4}, {5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 5}, {4, 5}, {2, 3,
4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}, {2, 3, 4, 5}

7. a. ii b. i

c. ii
d. iii

8. A’ = {1, 3, 5,
7, 9}

9. a. Finite set

b. Singleton set

c. Infinite set

d. Empty set

**Worksheet 2**

1. a. A = {2, 4,
6} b. 4

c.
equal d. Î¾

2. a. i. {1, 3,
7, 9, 13, 15, 17, 27}

ii. {3, 7, 13, 17}

iii. {3, 9, 15, 18, 27}

iv. {7, 14}

v. {1, 4, 7, 13, 14, 17, 27}

vi. {3, 7, 13, 17}

vii. {3}

b. n(A) = 8; n(B)
= 4; n(C) = 5; n(D) = 2

c. (A, B); (B, C);
(A, C); (A, D); (B, D)

3. a. iii b. iv c. i d. ii

4. a. False b. True

c. False d. True

e. True

5. a. {x: x is a
prime number less than 12}

b. {x: x = 7n; n *Ñ”* N; n ≤ 7}

c. {x:
x is a vowel of English alphabet}

d. {x:
x is a letter of the word PENCIL}

e. {x: x is a month of the year starting
with letter J}

6. a. 2^{5}
= 32 b. 2^{4} = 16

7. {}; {T}; {E};
{S}; {T, E}; {E, S}; {T, S}; {T, E, S}

8. a. i b. iii

c. iii
d. i

9. a. A and
C

b. n(A) = 13

c. {5, 6, 7, 8, 9, 10, 11, 12}

**Crossword**

**Across:
**4. Set 5.
Infinite

** **7. Equivalent 8.
Empty

9. Venn 10. Roster

**Down: **1. Proper 2. Disjoint

3. Singleton 6.
Universal

**MCQs Questions for Class 7 Maths**

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