Sets Class 7 ICSE Worksheets

# Sets Class 7 ICSE Worksheets

Sets Class 7 ICSE Worksheets play a very important role in strengthening the maths concepts.

## 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 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

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. 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 2with 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 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 is a prime number between 10 and 20}.

7. List the proper subsets of set A where A = {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. 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. 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