## 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.

## Frequently Asked Questions (FAQ)

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## Quiz on Finite Sets

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