Page 9 - Math 7

Set

1.4 Cardinal number of a set

Let's take a set of even numbers less than 12, i.e., E = {2, 4, 6, 8, 10}.
There are five members or elements in this set E. Therefore, the cardinal number of
the set E, denoted by n (E) = 5. Similarly, in A = {m, a, t, h}, its cardinal number
n (A) = 4. Thus, the number of members or elements contained by a set is known
as its cardinal number.

1.5 Types of sets
According to the number of elements contained by sets, there are four types of sets.

(i) Empty or null set (ii) Unit or singleton set (iii) Finite set (iv) Infinite set

(i) Empty or null set
There can be certain sets that do not contain any element at all. For example,
the sets of months with 35 days, the set of triangles with 4 sides, etc. do not
contain any element. So, the listing for these sets contains no element at all
and we call it an empty or null set.

Thus, a set containing no elements is called an empty or a null set. It is
represented by the symbol { } or I (Phi). Similarly,
if A = {natural numbers between 9 and 10}, A = { } or I and n(A) = 0.

if B = {whole numbers less than 0}, B = {} or I and n(B) = 0, and so on.
(ii) Unit or singleton set
Let's take a set A = {odd numbers between 8 and 10}.

Here, A = {9}. Thus, the set A contains exactly one element. Therefore, the
set A is called a unit or singleton set. A set containing exactly one element is
called a unit or singleton set.
Similarly,
if P = {prime and even numbers}, P = {2} and n(P) = 1
if Q = {x : 6 < x < 8, x ∈ N}, Q = {7} and n(Q) = 1, and so on.

(iii) Finite sets
Let's consider a set C = {composite numbers less than 10}.
Here, C = {4, 6, 8, 9} and we can count the number of elements of this set,
i.e. n(C) = 5. Hence, the set C is said to be a finite set.
Thus, a set containing finite number of elements is called a finite set.
Similarly,

if A = {1, 2,3, …, 20}, n(A) = 20
if B = {x : 2 < x < 31, x ∈ prime number}, n(B) = 9. It is a finite set.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 7 Vedanta Excel in Mathematics - Book 7