Page 86 - ICSE Math 7

Example 6: Write all the subsets of set {0, 2, 4}.
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Solution: There are 3 members in the given set. So, there will be 2 = 8 subsets.
The required subsets are f, {0}, {2}, {4}, {0, 2}, {2, 4}, {0, 4} and {0, 2, 4}.

Example 7: Write the set X = {x | 2x < 10} in roster form, when the universal set is:
(a) N, the set of natural numbers
(b) W, the set of whole numbers
(c) Z, the set of integers
Solution: (a) Every member of set X must belong to universal set N, such that 2x < 10.

So, x can be 1, 2, 3 and 4.
\ X = {1, 2, 3, 4}
(b) Every member of set X must belong to universal set W, such that 2x < 10.

So, x can be 0, 1, 2, 3 and 4.
\ X = {0, 1, 2, 3, 4}
(c) Every member of set X must belong to universal set Z, such that 2x < 10.
So, x can be 0, 1, 2, 3, 4 and any negative integer.
\ X = {..., –2, –1, 0, 1, 2, 3, 4}

Exercise 6.2

1. Classify the following sets as finite, infinite and null sets.
(a) X = {x | x + 3 = 1, x ∈ N} (b) X = {x | x + 5 = 5, x ∈ W}
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(c) y = {x | 2x < 5, x ∈ Z} (d) Z = {y | y = n , n ∈ N}

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(e) A = {x | x < 0, x ∈ W} (f) B = {y | y = 4, y ∈ Z}
2. Find the cardinal number of the following sets.
(a) A = {x | x is a consonant in the word VOWEL}
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(b) X = {x | x – 25 = 0, x ∈ Z}

(c) Y = {y | y is a letter of the word EDUCATION}
(d) Z = {x | x is an even factor of 12}
(e) B = {x | x is a one-digit prime number}

3. Let A = {1, 2, 3}, B = {4}, C = {3, 4}, D = {1, 2, 4} and E = {1, 2}.
Determine if the following statements are true or false.
(a) E ⊂ A (b) B ⊂ C (c) A ⊆ D (d) B ⊂ D

(e) A = E (f) C ↔ E (g) A ↔ B (h) A ↔ D
4. Write the subsets of the following sets.
(a) f (b) {a} (c) {a, b}
5. Find the number of subsets of the following sets.

(a) f (b) {Bombay} (c) {3, 5, 7} (d) {1, 2, 4, 6, 8}
6. Write the set X = {x | 2x + 1 < 14}, when the universal set is:
(a) N (b) W (c) Z

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