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JUPITER SCIENCE

Subset

If there are two sets A & B such that every element of A is also in B, then A is called a subset of B. In other words, A is contained in B


B is called the superset of A. In the set theory, this relationship is depicted as below

A ⊆ B ( A is a subset of B)

B ⊇ A ( B is a superset of A )

⇒ ∅ (empty set) is the subset of every set

⇒ A set S is a subset of itself.

Examples ⇒

{ 1 } ⊆ { 1, 2, 3 }

∅ ⊆ { 1, 2, 3 }

{ 1, 2, 3 } ⊆ { 1, 2, 3 }

{ x2 | x ∈ N } ⊆ N ( N is set of all natural numbers )

{ x3 | x ∈ Z } ⊈ N

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