Sets Class 7 ICSE Worksheet 1 with Answers
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 = 2n, 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 = 2n – 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.
ξ = {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 with Answers
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 ξ is the universal set and Q is the null set, then Q′ is equal to ___________.
2.
Given ξ = {1, 3, 4, 7, 9, 13, 14, 15, 17, 18,
27},
A
= { x: x є ξ, x is
an odd number},
B
= { x: x є ξ, x is a prime number},
C = { x: x є ξ, x is a multiple of 3} and
D = { x; x є ξ, 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.
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. ξ
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. 25
= 32 b. 24 = 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
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