Flashcards
Logic I
Flashcards do conjunto (36)
- 1Axiom of ExtensionalityIf sets x and y have exactly the same numbers then x is the same set as y
- 2Axiom of Naïve ComprehensionFor any property P there is a set (the extension) of all and only the things satisfying P
- 3Union (of sets A and B)All x such that x is a member of A or a member of B (or both)
- 4Intersection (of sets A and B)All x such that x is a member of A and B
- 5Set Difference (Subtraction) A\B (A-B)All x such that x is in A and not in B
- 6Symmetric DifferenceThe union of A\B and B\A
i.e. all x such that it is in only A or B - 7Families of setse.g. let F be the set of some sets V
e.g. the union of F is all x such that x is a member of some V - 8A is a subset of Biff for all z that is a member of A is a member of B also
- 9A is a proper subset of Biff A is a subset of B but B is not a subset of A
- 10A is identical to Biff A is a subset of B and B is a subset of A
- 11The powerset of A P(A)is the set of all the subsets of A
- 12The pairing{{x},{x,y}}
- 13Cartesian Product AxBthe set of all ordered pairs where the first element is from A and the second from B
- 14RelationA set of ordered pairs
- 15Dom(R) for AxBAll a that is a member of A s.t. there is a b (a member of B) that pairs with a
- 16Ran(R) for AxBAll b that is a member of B such that there is an x (that is a member of A) that pairs with b
- 17Inverse of R (where R is a subset of AxB)All the pairs that are members of BxA such that is a member of R
- 18Relation R is reflexiveiff aRa for all of a that is a member of A
- 19Relation R is irreflexiveiff aRa for no a that is a member of A
- 20R is symmetriciff aRb implies bRa for all a that is a member of A and all b that is a member of B
- 21Relation R is asymmetriciff aRb implies not bRa
- 22Relation R is antisymmetriciff aRb and bRa implies a=b
- 23R is transitiveiff aRb and bRc then aRc
- 24R is intransitiveiff aRb and bRc then not aRc
- 25R is connectediff either aRb or bRa for all a and b in A
- 26R is a pre-orderiff R is reflexive and transitive
- 27R is a weak partial-orderiff R is reflective, antisymmetric and transitive
- 28R is a strict-partial orderiff R is irreflexive, asymmetric and transitive
- 29R is a linear orderiff R is reflexive, antisymmetric and conneted
- 30R is an equivalence relationiff R is reflexive, symmetric and transitive
- 31a in A is minimaliff there is no b in A that is less than a
- 32a in A is leastiff for all b in A a is less than b
- 33a in A is maximaliff there is no b in A that is greater than a
- 34a in A is greatestiff for all b in A b is less than a
- 35Linear orderA well order with a least element
- 36Partial order is well-foundediff there is a least element
Informações
- Descrição
- (Logic) FlashCards sobre Logic I, criado por kirsty.a.paton em 28-04-2014.
- Criado por
- kirsty.a.paton
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