Maths > Set Theory > 1.0 Set
Set Theory
1.0 Set
2.0 Representation of set
3.0 Types of set
4.0 Subsets
5.0 Theorems based on Subsets
6.0 Power set
7.0 Subsets of the Set $R$
8.0 Intervals as subsets of $R$
9.0 Universal set
10.0 Venn Diagrams and operation on sets
11.0 Laws of algebra of sets
12.0 Number of elements in sets
1.1 Elements of a set
The members of a set are called its elements.
A set is usually denoted by capital letters $A$, $B$, $C$ etc. whereas elements are generally denoted by lower case letters $a$, $b$, $c$ etc.
If an element $x$ is in set $A$, we say that $x$ belongs to $A$, i.e. $$x \in A$$
If the element $x$ does not belong to $A$ then it is written as $$x \notin A$$
Element of a set can also be called as member or object of a set.
Illustration 2. Write down the elements of the following sets.
a. Collection of vowels in the alphabet of English language
b. Set of months that begin with "J"
c. Set of all natural prime numbers.
d. The solution of the equation ${x^3} + 10{x^2} + 7x - 18=0$
e. Set of all alphabets used to form "EDUCATION"
f. The collection of all odd numbers
Solution:
| SET | ELEMENTS |
| a. Collection of vowels in the alphabet of English language | This set is well defined and we know that there are only five of them. The elements are $a, e, i, o, u$ |
| b. Set of months that begin with "J" | The elements are $January, June, July$ |
| c. Set of all natural prime numbers | The elements are $2, 3, 5, 7, 11, 13, ........ $ |
| d. The solution of the equation ${x^3} + 10{x^2} + 7x - 18=0$ | The equation ${x^3} + 10{x^2} + 7x - 18=0$ can be factorised as, $$\begin{equation} \begin{aligned} (x - 1)({x^2} + 11x + 18) = 0 \\ (x - 1)(x + 2)(x + 9) = 0 \\\end{aligned} \end{equation} $$ Hence the solutions are, $1, -2, -9$ Thus the elements are $1, -2, -9$ |
| e. Set of all alphabets used to form "EDUCATION" | The elements are $e, d, u, c, a, t, i, o, n$ |
| f. The collection of all odd numbers | The elements are $1, 3, 5, 7, ......$ |
