Types of Sets Mathematics – Empty & Equal Sets

Set is defined as a collection of objects. There are many types of sets in mathematics which are given below.

Types of Sets

1). Empty Set

A set is said to be empty or null or void set if it has no element and it is denoted by \(\phi\).

for example : The set A is given by A = [ x : x is an even prime number greater than 2 ] is an empty set because 2 is the only even prime number.

2). Singleton Set

A set consisting of a single element is called a singleton set.

for example : The set {5} is a singleton set.

3). Finite Set

A set is called finite set if it is either void set or its element can be listed by the natural numbers 1, 2, 3 ….. n for any natural number n.

for example : The set of even natural numbers less than 100.

4). Infinite Set

A set whose elements cannot be listed by the natural numbers 1, 2, 3 ….. n for any natural number n is called infinite set.

for example : The set of all points in a plane.

5). Equivalent Sets

Two finite sets A and B are said to be equivalent if their cardinal numbers are same i.e. n(A) = n(B).

for example : If A = { 1, 2 } and B = { 3, 4 }, both are equivalent as cardinality of A is equal to the cardinality of B. i.e. |A| = |B| = 2.

6). Equal Sets

Two sets A and B are said to be equal if every element of A is a member of B, and every element of B is a member of A.

If sets A and B are equal, we write A = B and A \(\ne\) B when A and B are not equal.

for example : If A = { 1, 2, 5, 6 } and B = { 5, 6, 2, 1 }, then A = B, because each element of A is an element of B and vice versa.

7). Subsets

Let  A and B be two sets. If every element of A is a element of B, then A is called a subset of B.

If A is a subset of B, we write A \(\subset\) B, which is read as “A is a subset of B”.

for example : If A = { 1 } and B = { 3, 2, 1 }, then A \(\subset\) B, because every element of A is an element of B.

8). Universal Set

A set that contains all sets in a given context is called universal set.

for example : when we are using sets containing natural numbers, then N is the universal set.

9). Power Set

Let A be a set. Then the collection or family of all subsets of A is called the power set of A and is denoted by P(A).

Since the empty set and set A itself are subsets of A and are therefore elements of P(A). Thus the power set of a given set is always non-empty.

for example : Let A = {1, 2}. Then the subsets of A are :

\(\phi\), {1}, {2}, {1, 2}

Hope you learnt types of sets in mathematics , learn more concepts of sets  and practice more questions to get ahead in the competition. Good luck!

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