The following topics are immediate subtopics of Set Theory.

Term: Axiom Of Choice
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 Definition: Given a collection S of disjoint nonempty sets, there exists a set C consisting of exactly one element from each element of S; that is, a set C such that C is contained in the union of S, and for e...

Term: Bijective
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 Definition: If a function is both injective and surjective, it is said to be bijective (or is called a onetoone correspondence).

Term: Cardinality
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 Definition: The cardinality of a set is the cardinal number indicating the number of elements in the set.

Term: Cartesian Product
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 Definition: The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b in B. It is denoted AxB...

Term: Choice Function
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 Definition: Given a collection B of nonempty sets (not necessarily disjoint), there exists a function c:B > {arbitrary union A, where A is in B} such that c(A) is an element of A, for each A in B. The functi...

Term: Conclusion
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 Definition: In a statement of the form, "If P, then Q," Q is called the conclusion of the statement.

Term: Converse
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 Definition: Given a statement "P implies Q," the converse would be "Q implies P." A converse of a statement is not necessarily true.

Term: De Morgan's Laws
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 Definition: The complement of the union equals the intersection of the complements. The complement of the intersection equals the union of the complements.

Term: Dictionary Order Relation
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 Definition: Suppose that A and B are two sets with order relations <_A and <_B respectively. Define an order relation < on AxB by defining (a_1)x(b_1) < (a_2)x(b_2) if a_1 <_A a_2, or if a_1 = a_2 and b_1 <_B...

Term: Disjoint
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 Definition: Two sets are disjoint if they have no elements in common. In other words, two sets are disjoint if their intersection equals the empty set.