Math | Class XI | Set Theory | 01| JEE Mains ADVANCED - Videos

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Sets are used to define the concepts of relations and functions. We are going to study about different types of sets, venn diagrams, and operations on sets.

In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}.

The different types of sets are explained below with examples.

Empty Set or Null Set:

A set which does not contain any element is called an empty set, or the null set or the void set and it is denoted by ∅ and is read as phi. In roster form, ∅ is denoted by {}. An empty set is a finite set, since the number of elements in an empty set is finite, i.e., 0.

For example: (a) The set of whole numbers less than 0.

(b) Clearly there is no whole number less than 0.

Therefore, it is an empty set.

∅ ≠ {0} ∴ has no element.

{0} is a set which has one element 0.

The cardinal number of an empty set, i.e., n(∅) = 0

Singleton Set:

A set which contains only one element is called a singleton set.

For example:

• A = {x : x is neither prime nor composite}

It is a singleton set containing one element, i.e., 1.

A set which contains a definite number of elements is called a finite set. Empty set is also called a finite set.

For example:

• The set of all colors in the rainbow.

Infinite Set:

The set whose elements cannot be listed, i.e., set containing never-ending elements is called an infinite set.

For example:

• Set of all points in a plane

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