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Set Theory Notations
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Flashcards
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A ⊂ B
A is a proper subset of B; A is a subset of B but A is not equal to B.
A ⊆ B
A is a subset of B; every element of A is also in B.
A ∩ B
The intersection of sets A and B; the set of elements that are in both A and B.
A ∪ B
The union of sets A and B; the set of all elements that are in A, in B, or in both.
A × B
The Cartesian product of A and B; the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.
A ∆ B
The symmetric difference between sets A and B; the set of elements that are in either A or B, but not in both.
A - B
The difference between sets A and B; the set of elements that are in A but not in B.
ℙ(A)
The power set of A; the set of all subsets of A, including A itself and the empty set.
a ∈ A
Element 'a' is a member of set A.
∅
The empty set; the set with no elements.
A = B
Set equivalence; A and B have exactly the same elements.
|A|
The cardinality of set A; the number of elements in set A.
A ⊃ B
A is a superset of B; every element of B is also in A.
A ⊖ B
Another notation for the symmetric difference between sets A and B; the set of elements in either A or B, but not both.
A ≠ B
A is not equal to B; A and B do not have exactly the same elements.
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