# Subset, Equality of Set, Proper Subset

If every element of a set is also an element of a set , the is called a subset of and it is denoted as .

Example:

Note:

Hence is the superset of .

Equality of Sets:

If every element of belongs to and every element of belongs to , i.e., if and only if

or

Example:

Proper Subset:

If every element of the set is an element of the set and contains at least one element which does not belongs to , i.e., and .

Example:

.

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