Page 91 - ICSE Math 7

3. Write the cardinal number of each of the following sets.
(a) A = Set of days of a week (b) X = Set of negative natural numbers
(c) Y = Set of letters in the word INFINITE (d) C = set of prime numbers divisible by 2

(e) B = {x | x ∈ Z and –3 ≤ x ≤ 3}
4. State the following pairs of sets as disjoint or overlapping.
(a) A = {0, 2, 3, 4, 6} and B = {odd numbers between 1 and 5}
(b) A = {natural numbers less than 20} and B = {multiples of 10}
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(c) A = {x | x = n , n ∈ N, n ≤ 5} and B = {x | x = n , n ∈ N, n ≤ 5}
(d) X = {x | 3x = 0, x ∈ W} and Y = {x | 2x = 2, x ∈ N}
(e) A = {x | x is a letter in the word MUMBAI} and B = {x | x is a letter in the word FOLLOW}

5. State the following pairs of sets as equal or equivalent.
(a) X = Set of first four natural numbers and Y = set of first four whole numbers
(b) A = {x | x is a letter in the word PROPER} and B = {x | x is a letter in the word ROPE}
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2
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(c) A = {1 , 2 , 3 , 4 } and B = {16, 9, 4, 1}
(d) X = {x | x is a day of the week starting with the letter S} and Y = {x | x is a month starting
with the letter M}
6. Write the set X = {x | 3x < 12} in the roster form, when the universal set is:
(a) N (b) W (c) Z
7. Write the number of proper subsets of the following sets.
(a) A = {1, 3, 5, 7} (b) X = f (c) Y = {1}
8. Write all the subsets of the set {5, 15, 25}.

9. If P and Q are two sets such that P ∪ Q has 65 elements, P has 38 elements and Q has 35 elements,
how many elements does P ∩ Q have?

10. The minimum height and weight of the player of a team must be 150 cm and 45 kg. Form a set
of students using the given table that can be selected as a player for the team.

Students Nishant Alisha Gitika Naman Pooja Anuj

Height 156 cm 152 cm 154 cm 155 cm 152 cm 149 cm
Weight 46 kg 44 kg 45 kg 48 kg 46 kg 46 kg

11. Out of a group of 70 people, 37 people like Hindi movies, 52 like English movies and each person
likes at least one of the two movies. Find the number of people who like:
(a) both the movies (b) only English movies
12. In a village there are 850 people who speak Hindi or Bengali. Out of these 675 people speak
Hindi and 200 people speak both the languages. How many people speak Bengali? How many
people speak only Hindi?

THINK SMART

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1. Write X = {x | x = , n ∈ N, n ≤ 12} in the roster form and find the cardinality of X.
n
2. If U = {6, 12, 18, 24, 30, 36, 42, 48}, A = {12, 24, 36, 48} and B = {6, 12, 30, 42, 48}, then find:

(a) U – (A ∩ B) (b) (A ∪ B) – (A ∩ B) (c) (A ∪ B) – A (d) U – (A ∪ B)

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