There are various types of sets:

• Finite Set

• Infinite Set

• Null Set

• Singleton Set

• Equivalent Sets

• Equal Sets

Finite Set

$A$ set is said to be finite if it contains only finite number of elements.

Let $A$ = $\{ 1, 2, 3, 4, 5 \}$

$B$ = $\{ a, b, c, d, e, f \}$

Here, $A$ contains $5$ elements and $B$ contains $6$ elements. So, $A$ and $B$ are finite sets

**Examples of Finite Set**

• The set $\{ 2, 4, 6 \}$ Is a finite set, as it contains only $3$ elements.

• If $A$ is the set of all days in a week, then $A$ is a finite set containing $7$ elements.

Infinite Set

$A$ set is said to be infinite if it contains an infinite number of elements.

Let $C$ = {number of men living in different parts of the world}

It is difficult to find the number of elements in $C$. But, it is a definite number, may be quite a big number. And so, $C$ is an infinite set.

**Examples of Infinite Set**

• The set of all even numbers is an infinite set.

• The set of points on a particular straight line is an infinite set.

• The sets $N$ (Natural Numbers), $Z$ (Integers), $Q$ (Rational Numbers), $R$ (Real Numbers) and $C$ (Complex Numbers) are all infinite sets, where:

1) $N$ = $\{ 1, 2, 3, 4, ....................... \}$

2) $Z$ = $\{ .............., -3, -2, -1, 0, 1, 2, 3, .......... \}$

3) $Q$ = $\{$ $\frac{(p)}{(q)}$ : $p, q$ in $Z, q \notin 0 \}$

4) $R$ = $\{ x : " x$ is either a rational number or an irrational number " $\}$

5) $C$ = $\{ x + iy : x, y$ in $R, i$ = $\sqrt{-1} \}$

Null Set

A set is said to be a null set if it does not contain any element. A null set is also called as an empty set or void set. A null set is denoted by $\phi$.

Therefore, $\phi$ = $\{ \}$

The set $\{ 0 \}$ is not a null set, because this set contains one element "$0$".

**Examples of Null Set**

• Let $A$ = $\{ x : x\ \epsilon\ N, 2 < x <3 \}$. $A$ does not contain any element , because there is no natural number between $2$ and $3$.

• Let $B$ = $\{ x : x\ \epsilon\ Q, 2 < x < 3 \}$. $B$ is not a null set, because rational numbers like $\frac{5}{2}$, $\frac{7}{3}$, $\frac{9}{4}$, $\frac{11}{5}$, ....... are all elements of the set $B$.

Singleton Set

A set is said to be a singleton set, if it contains only one element.

**Examples of the Singleton Set**

• The set $\{ 7 \}$ , $\{ -15 \}$ are singleton sets.

• $\{ x : x + 4 = 0, x\ \epsilon\ Z \}$ is a singleton set, because this set contains only one integer namely, $-4$.

Equivalent Sets

Two sets $A$ and $B$ are said to be equivalent sets if the elements of $A$ can be paired with the elements of $B$, so that each element of $A$ corresponds exactly to one element of $B$, and each element of $B$ there corresponds exactly to one element of $A$.

**Examples of Equivalent Sets**

• The sets $\{ a, b, c \}$ and $\{ 4, 7, 10 \}$ are equivalent.

• The sets $\{ w, x, y, z \}$ and $\{ 1, 2, 3, 4 \}$ are equivalent.

Equal Sets

Two sets are said to be equal sets if every element of one set is in the other set and vice-versa. So, two sets are equal, if $x$ in $A \Rightarrow x$ in $B$ and $x\ \epsilon\ B \Rightarrow x\ \epsilon\ A$. If sets $A$ and $B$ are not equal, then we write $A \neq B$

**Examples of Equal Sets**

Let $A$ = $\{ x : x\ \epsilon\ N,\ 2 \leq x \leq 6 \}$ and $B$ = $\{ 2, 3, 4, 5, 6 \}$ , then $A$ = $B$

Let $A$ = $\{ x : x\ \epsilon\ N, 10 < x < 11 \}$ and $B$ = $\{ 10.5 \}$ , then $A \neq B$ since $10.5\ \epsilon\ A$