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If A is a subset of B but A ≠ B, then A is called the proper subset of B, and B is called the proper superset of A. This relationship is represented as below
A ⊂ B ( A is a proper subset of A )
B ⊃ A ( B is a proper superset of A )
Examples ⇒
{ x2 | x ∈ N } ⊂ N ( not all natural numbers are squares )
{ 1, 2, 3 } ⊂ { 1, 2, 3, 4 }
{ 1, 2, 3, 3 } ⊂ { 1, 2, 3, 4 }
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