Page 83 - ICSE Math 7

2. Write True or False.
(a) Sets {1, 3, 4, 5}, {5, 4, 3, 1} and {4, 5, 3, 1} are same.
(b) If X is a set of letters of the word ALGEBRA, then X = {A, L, E, B, R, A}.

(c) The set X of prime numbers in roster form is given by X = {2, 3, 5}.
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(d) A set of cubes of whole numbers in set-builder form is given by {x | x = n , n ∈ W}
(e) 20 ∈ {x | x = 4n, n ∈ N}
(f) 3 ∈ {x | x is a factor of 32}
3. Write the following sets in roster form.
(a) Set of odd natural numbers between 20 and 26.
(b) X = {x | x is a letter of the word EXTENSION}

(c) The set X of all composite numbers between 10 and 20.
(d) Y = {y | y ∈ N and y > 7}
(e) The set A of squares of first six whole numbers.
(f) The set of factors of 12.
4. Write the following sets in set-builder form.
(a) X = {10, 20, 30, ...} (b) A = {January, June, July}

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(c) Y = {21, 23, 25, 27, 29, 31, ...} (d) B = 1,, ,, 
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 2 3 4 5
Types of Sets

Finite set
A set is known as a finite set if it has a finite number of elements, i.e., countable number of elements.
For example,
(a) A = {x | x is a natural number less than 25} is a finite set as it has 25 elements.
(b) B = {x | x is a letter of English alphabet} is a finite set with 26 elements.
(c) C = {x | x = 3n, n ∈ N, n ≤ 12}

Infinite set
A set is known as an infinite set if it has an infinite number of elements, i.e., uncountable number of
elements. For example,
(a) The set of stars in the sky is an infinite set.
(b) X = {x | x is a composite number} is an infinite set.
(c) The set of positive integers.

Singleton set
A set is known as singleton set if it has only one element. For example,
(a) A = {a} is a singleton set as it has only one element, i.e., a.
(b) A set of even prime number is a singleton set as it has only one member, i.e., 2.

Empty set
A set which contains no element is called an empty set or null set. It is denoted by f or {}. For example,
(a) X = {x | x < 1, x ∈ N} is an empty set as there is no natural number which is less than 1.
x x x
(b) A = {x | + 2 = 1, x ∈ W} is an empty set as + 2 = 1 ⇒ = –1 ⇒ x = – 3 ∉ W
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