Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Subset, Equality of Set, Proper Subset

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

Example: 

A= \{2,4,5,9,11\}, B= \{2,4,5,9,11\}

A \subseteq B

Note:

Hence   B is the superset of  A .

Equality of Sets:

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

x \in A\Leftrightarrow x\in B or  A\subset B, B\subset A \Leftrightarrow A = B

Example:

A = \{4,9,3,5\}, B=\{3,4,5,9\}

 \therefore  A=B

Proper Subset:

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

Example:

A=\{2,3,4\}, B= \{2,3,4,5\}

 \therefore A\subset B .

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