Page 90 - ICSE Math 7

¾ Two sets are said to be equivalent if the number of elements in both the sets is same.

¾ Two sets are said to be disjoint if they have no common element.
¾ Two sets are said to be overlapping if they have at least one common element.
¾ The number of elements in a finite set is known as its cardinal number.
¾ X is a subset of Y if every member of X is also a member of Y. If there exists at least one member
of Y which is not in X, then X is known as a proper subset of Y.
n
n
¾ If a set has n elements, then it has 2 subsets and 2 – 1 proper subsets.
¾ A set which contains all the given sets as its subsets is known as a universal set.
¾ For any non-empty sets A and B
• n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
• When A and B are disjoint sets, A ∩ B = f. Therefore, n(A ∪ B) = n(A) + n(B)

• n(A – B) = n(A) – n(A ∩ B)
• n(B – A) = n(B) – n(A ∩ B)

MENTAL MATHS

1. Write True or False.
(a) Equivalent sets are always equal.

(b) Every set is a subset of a null set.
25
(c) If a set has 25 elements, then the number of its subsets is 2 .
(d) Every set is a proper subset of itself.

(e) The cardinal number of set A = {0} is 1.
(f) The number of subsets of a null set is 2.
2
2. Let X = {2, –2}, Y = {x | x = 4, x ∈ Z} and A = {–2, 0, 2}. State which of the following are true
and which are false.

(a) X ⊆ Y (b) Y ⊆ X (c) A ⊆ X (d) X = Y (e) Y ⊂ A
3. Let A be the set of natural numbers which are multiples of 6 and less than 30. Fill in the blanks
using ∈ or ∉.
(a) 12 ____ A (b) 36 ____ A (c) 30 ____ A (d) 24 ____ A

PRACTICE TIME

1. Write the following sets in the roster and set-builder form.
(a) The set X of vowels of the word NATURAL
(b) The set Y of even natural numbers lying between 5 and 13

(c) The set A of odd numbers lying between 10 and 20
2. Let A = {x | x is a letter in the word EQUIVALENT}, B = {x | x is a letter in the word EQUAL}
and C = {x | x is a letter in the word TALENT}. Prove that:
(a) B ⊆ A (b) C ⊂ A (c) B ↔ C

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