Subset Calculator

 
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The set B is = of set A

In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.

The subset relation defines a partial order on sets. The algebra of subsets forms a Boolean algebra in which the subset relation is called inclusion.

If A and B are sets and every element of A is also an element of B, then: A is a subset of (or is included in) B, denoted by A ⊆ B

Some basic properties of unions:

 

  • A ∪ B = B ∪ A.
  • A ∪ (B ∪ C) = (A ∪ B) ∪ C.
  • A ⊆ (A ∪ B).
  • A ∪ A = A.
  • A ∪ ∅ = A.
  • A ⊆ B if and only if A ∪ B = B.

 

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