# Finite Sets

## Definition of Finite Sets

The meaning of the word ‘Finite’ is ‘having a definite limit or fixed size’. Therefore, the Finite Sets may be defined as the sets that have a definite number of elements or a countable number of elements in them.

In other words, a set $A$ is said to be a Finite Set if it has a definite or countable number of elements present in it. Therefore, Finite Sets have a finite number of elements. Also, the Cardinality of a Finite Set is Finite.

## Finite Set Examples

The above figure shows the $3$ sets $A, B$ and $C$. The elements of the three sets are,

• $A = \{1, 2, 3, 4, 5\}$
• $B = \{b, c, d, f\}$
• $C = \{1, 2, 3, ......., 30\}$

All the sets $A, B$ and $C$ in the above examples have a finite number of elements. The set $A$ has $5$ elements, the set $B$ has $4$ elements and the set $C$ has $30$ elements. Therefore, the above sets are Finite Sets.

## Practical Examples of Finite Sets

• Set of all the months in a year.

We are well aware that there are 12 months in a year i.e., January, February, March, April, May, June, July, August, September, October, November and December. Therefore, the set of all the months in a year has a definite number of elements i.e., 12 and hence it is a Finite Set.

• Set of all the days in a week.

Similarly, there are seven days in a week viz., Sunday, Monday, Tuesday, Wednessday, Thursday, Friday and Saturday. Therefore, the set of all the days in a week has a definite number of elements that is 7 and hence it is a Finite Set.

• Set of all the planets in our solar system.

The set of all the planets in our Solar System is also Finite Set because the solar system has a Finite number (8) of planets viz., Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.

• Set of all the elements in the periodic table.

The set of all the elements in the Periodic Table is Finite Set because it has 118 number of elements.

• Set of all the books for class 10.

## Properties of a Finite Set

The properties of a Finite sets are as follows:

• The Subset of a Finite Set is always a Finite Set.
• The Superset of a Finite Set may be finite or infinite.
• The Union of two Finite Sets is always a finite set.