Page 83 - ICSE Math 8

2. Put the correct sign of ‘=’ or ‘↔’ in the blanks.
(a) {a, e, i, o, u} _____ {x : x is a vowel of English alphabet}
(b) {6, 8, 9,11} _____ {8, 6, 11, 7}
(c) {x : x is a prime number < 15} _____ {2, 3, 5, 7, 11, 13}
(d) {x : x = 3n, n ∈ N, n < 4} _____ {x : x = n + 3, n ∈ N, n < 4}
3. Write True or False.
(a) φ ⊂ {a, b, c} (b) {1} ∈ {1, 4, 9, 16}
(c) 3 ∈ {x : x ∈ Z, –3 ≤ x ≤ 2} (d) For disjoint sets A and B, A – B = A.
(e) For two sets A and B, (A – B) ∩ (B – A) = φ.

PRACTICE TIME

1. Find the cardinal number of the following sets.
(a) X = {–5, –4, 4, 5} (b) Y = {x : x ∈ W, 0 < x ≤ 5}
(c) A = {x : x is a letter of the word APPRECIATE} (d) B = {x : x = 3y – 2, y ∈ N, y < 3}
2. State which of the following sets are finite and which are infinite.
(a) P = {x : x ∈ N, x > 5} (b) Q = {x : x = 4y – 2, y ∈ N, y > 3}
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(c) X = {x : x is a factor of 150} (d) Y = {x : x = 2n + 1, n ∈ N, n ≤ 13}
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3. Are the sets A = {1, 2, 3, 4} and B = {x : x – 16 = 0} disjoint?
4. State whether the following pairs of sets are equal or equivalent.
(a) X = {x : 2x + 1 ≤ 12, x ∈ N} and Y {x : x + 2 < 7, x ∈ W}
(b) P = {x : x is a letter of the word APPEAL} and Q = {x : x is a letter of the word LEAP}
(c) A = {x : x is a factor of 20} and B = {x : x is a factor of 12}
5. Find the number of proper subsets of the following sets.
(a) {3} (b) φ (c) {0, 2, 4} (d) {a, b, c, d, e}
6. A set has 8 possible subsets, find the cardinal number of the set.
7. A set has 63 possible proper subsets, find the cardinal number of the set.
8. Using set theory, find the HCF of 9 and 36.
9. Using set theory, prove that the following pairs of numbers are prime to each other.
(a) 15, 24 (b) 30, 49
10. If P = {factors of 36} and Q = {factors of 42}, find:
(a) P ∪ Q (b) P ∩ Q (c) P – Q (d) Q – P
11. If n(X) = 35, n(Y) = 42 and n(X ∩ Y) = 9, find:
(a) n(X ∪ Y) (b) n(X – Y)
12. Given U = {x : 10 ≤ x ≤ 15, x ∈ N}, A = {x : x < 12, x ∈ N} and B = {x : 9 < x < 15, x ∈ N}, verify that:
(a) (A ∪ B)′ = A′ ∩ B′ (b) (A ∩ B)′ = A′ ∪ B′

THINK SMART

Rohan’s friends list is given by a set A = {Rishi, Kavya, Raj, Arnav, John, Chris, Shreya} and Adil’s friends
list is given by a set B = {Shikha, Saya, Rishi, Navdeep, Chris, Arnav}. Can you find their mutual friends
using properties of sets?

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