| Метод |
Описание |
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dataProviderForSingleSet ( ) |
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dataProviderForThreeSets ( ) |
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dataProviderForTwoSets ( ) |
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dataProviderForTwoSetsDifferent ( ) |
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testACartesianProductWithEmptySetIsEmptySet ( Set $A ) |
Axiom: A × Ø = Ø
A cartesian product with empty set is the empty set |
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testACrossUnsionBCEqualsACrossBUnionACrossC ( Set $A, Set $B, Set $C ) |
Axiom: A × (B ∪ C) = (A × B) ∪ (A × C)
A cross union of B and C is the union of A cross B and A cross C |
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testADiffBDifferentFromBDiffAWhenNotEqual ( Set $A, Set $B ) |
Axiom: A ∖ B ≠ B ∖ A for A ≠ B
A diff B does not equal B diff A if A and B are different sets |
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testADiffItselfIsEmptySet ( Set $A ) |
Axiom: A ∖ A = Ø
A diff itself is the empty set |
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testAIntersectionAEqualsA ( Set $A ) |
Axiom: A ∩ A = A
A intersection A equals A |
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testAIntersectionBIsSubsetOfA ( Set $A, Set $B ) |
Axiom: (A ∩ B) ⊆ A
A intersect B is a subset of A |
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testAIntersectionEmptySetIsEmptySet ( Set $A ) |
Axiom: A ∩ Ø = Ø
A union empty set is A |
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testAIsSubsetOfAUnionB ( Set $A, Set $B ) |
Axiom: A ⊆ (A ∪ B)
A is a subset of A union B |
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testASymmetricDifferentBEqualsUnionADiffBAndBDiffA ( Set $A, Set $B ) |
Axiom: A Δ B = (A ∖ B) ∪ (B ∖ A)
A symmetric different B equals union of A diff B and B diff A |
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testAUnionAEqualsA ( Set $A ) |
Axiom: A ∪ A = A
A union A equals A |
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testAUnionEmptySetEqualsA ( Set $A ) |
Axiom: A ∪ Ø = A
A union empty set is A |
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testAUnsionBCrossCEqualsUnsionOfACRossCAndBCrossC ( Set $A, Set $B, Set $C ) |
Axiom: (A ∪ B) × C = (A × C) ∪ (B × C)
A union B cross C is the union of A cross C and B cross C |
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testCardinalityOfCartesianProduct ( Set $A, Set $B ) |
Axiom: |A × B| - |A| * |B|
The cardinality (count) of the cartesian product is the product of the cardinality of A and B |
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testCardinalityOfPowerSet ( Set $A ) |
Axiom: |S| = n, then |P(S)| = 2ⁿ
The cardinality (count) of a power set of S is 2ⁿ if the cardinality of S is n. |
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testCardinalityOfUnion ( Set $A, Set $B ) |
Axiom: |A ∪ B| = |A| + |B| - |A ∩ B|
The cardinality (count) of unsion of A and B is equal to the cardinality of A + B minus the cardinality of A intersection B |
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testEmptySetSubsetOfEverySet ( Set $A ) |
Axiom: Ø ⊆ A
The empty set is a subset of every set |
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testEqualSetsAreSubsetsInBothDirections ( Set $A ) |
Axiom: A = B iff A ⊆ B and B ⊆ A
Sets are equal if and only if they are both subsets of each other. |
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testIntersectionAbsorbtion ( Set $A, Set $B ) |
Axiom: A ∩ (A ∪ B) = A
Intersection absorbtion law |
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testIntersectionAssociative ( Set $A, Set $B, Set $C ) |
Axiom: A ∩ (B ∩ C) = (A ∩ B) ∩ C
Intersection is associative |
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testIntersectionCommutative ( Set $A, Set $B ) |
Axiom: A ∩ B = B ∩ A
Intersection is commutative |
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testIntersectionDistributive ( Set $A, Set $B, Set $C ) |
Axiom: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Intersection is distributive |
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testSetIsSubsetOfItself ( Set $A ) |
Axiom: A ⊆ A
Every set is a subset of itself |
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testUnionAbsorbtion ( Set $A, Set $B ) |
Axiom: A ∪ (A ∩ B) = A
Union absorbtion law |
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testUnionCommutative ( Set $A, Set $B ) |
Axiom: A ∪ B = B ∪ A
Union is commutative |
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testUnionDistributive ( Set $A, Set $B, Set $C ) |
Axiom: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Union is distributive |
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testUnsionAssociative ( Set $A, Set $B, Set $C ) |
Axiom: A ∪ (B ∪ C) = (A ∪ B) ∪ C
Unsion is associative |
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