Page 84 - ICSE Math 7

Equal sets
Two sets are said to be equal if they have the same elements. If sets X and Y are equal, then we
write set X = set Y or X = Y. For example, if X = {x | x is a letter in the word FOLLOW} and
Y = {x | x is a letter in the word FOWL} then X = {F, O, L, W} and Y = {F, O, W, L}. So, X = Y.

Equivalent sets
Two sets are said to be equivalent if the number of elements in both Maths Info
the sets is same. For example, if X = {1, –1, 0} and Y = {a, b, c} then Two infinite sets are always
set X ↔ set Y (read as set X is equivalent to set Y) or X ↔ Y. equivalent.

Point to remember
Equal sets are always equivalent but converse is not always true.

Disjoint sets
Two sets are said to be disjoint if they have no common element. For example, if A = {1, 2, 3, 4, 5} and
B = {6, 7, 8, 9, 10}, then A and B are disjoint sets.

Overlapping sets
Two sets are said to be overlapping if they have at least one common element. For example, if
X = {x | x is a letter in the word INDIGO} and Y = {x | x is a letter in the word GREEK} then X and
Y are overlapping sets as both contain the element G.

Cardinal Number Maths Info

The number of distinct elements in a finite set is known as its cardinal If the cardinality of a set is 1,
number. The cardinal number of an empty set is 0 and cardinal number we call it a singleton set and if
of an infinite set is not defined. The cardinal number of a set say Y, is the cardinality is 2, we call it a
denoted by n(Y). For example, pair set.

(a) If X = {Delhi, Mumbai, Chennai}, then n(X) = 3.
(b) Let P be the set of letters of the word ‘SUNNY’, then P = {S, U, N, Y} has 4 distinct elements and so
P(n) = 4. So that the cardinal number of the given set is 4.
Example 4: Identify the finite and infinite sets among the following. Write the cardinal number of
the finite sets.
2
(a) X = {1, 3, 5, 7,..., 49} (b) Y = {x | x = n + 1, n ∈ N}
(c) Y = {x | x = 2n, n ∈ W, n < 4} (d) X = {x | x > 5, x ∈ N}
Solution: (a) Set X consists of all the odd natural numbers less than 50. So, X is a finite set.
Also n(X) = 25
(b) The set of natural numbers is an infinite set. So, set Y is also an infinite set.

(c) For n = 0, x = 2 × 0 = 0
For n = 1, x = 2 × 1 = 2
For n = 2, x = 2 × 2 = 4
For n = 3, x = 2 × 3 = 6

\ Y = {0, 2, 4, 6}. Thus Y is a finite set.
Also n(Y) = 4
(d) In roster form, X = {6, 7, 8, 9,...}. So, X is an infinite set.

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