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Relation (mathematics) - Quiz
Contributed by: French
  • 1. A relation is asymmetric if and only if it is which two of the following?
A) Symmetric and transitive
B) Strongly connected and total
C) Antisymmetric and irreflexive
D) Reflexive and connected
  • 2. A transitive relation is irreflexive if and only if it is what?
A) Symmetric
B) Reflexive
C) Connected
D) Asymmetric
  • 3. A relation is reflexive if and only if its complement is what?
A) Symmetric
B) Irreflexive
C) Asymmetric
D) Reflexive
  • 4. A relation is strongly connected if and only if it is connected and what?
A) Asymmetric
B) Irreflexive
C) Symmetric
D) Reflexive
  • 5. A relation is equal to its converse if and only if it is what?
A) Reflexive
B) Transitive
C) Asymmetric
D) Symmetric
  • 6. A relation is connected if and only if its complement is what?
A) Reflexive
B) Transitive
C) Anti-symmetric
D) Symmetric
  • 7. What is the term for a relation over a single set X?
A) Dependency relation
B) Heterogeneous relation
C) Homogeneous relation
D) Subset relation
  • 8. A relation between members of two different sets is known as what?
A) Symmetric relation
B) Heterogeneous relation
C) Endorelation
D) Homogeneous relation
  • 9. Which of the following is an example of a tolerance relation?
A) Asymmetric relation
B) Irreflexive relation
C) Dependency relation
D) Strict order
  • 10. Which of the following is categorized as an equivalence relation?
A) Isomorphic
B) Dependency relation
C) Subset of
D) Greater than
  • 11. An independency relation is defined as the complement of what?
A) A dependency relation
B) An equivalence relation
C) A strict order
D) A homogeneous relation
  • 12. If a relation's converse is transitive, what must the relation be?
A) Transitive
B) Asymmetric
C) Symmetric
D) Irreflexive
  • 13. A total order is defined as reflexive, antisymmetric, transitive, and what other property?
A) Functional
B) Connected
C) Symmetric
D) Serial
  • 14. A many-to-many relation is defined as what?
A) Functional and not injective
B) Injective and not functional
C) Not injective nor functional
D) Injective and functional
  • 15. In the notation S ∘ R, what does this operation represent?
A) The union
B) The relative product
C) The converse
D) The complement
  • 16. If R is a relation over X and Y, what is its converse relation RT?
A) {(x, y) | xRy}
B) {(y, x) | xRy}
C) {(y, x) | not xRy}
D) {(x, y) | not xRy}
  • 17. What is the complementary relation of R?
A) {(x, y) | not xRy}
B) {(y, x) | xRy}
C) {(y, x) | not xRy}
D) {(x, y) | xRy}
  • 18. A function is defined as a relation that is both functional and what?
A) Total
B) Injective
C) Symmetric
D) Surjective
  • 19. A bijection is a function that is both injective and what?
A) Total
B) Functional
C) Transitive
D) Surjective
  • 20. In the context of relations, when is R said to be smaller than S?
A) If R is the union of S
B) If R equals S
C) If S is contained in R but R is not contained in S
D) If R is contained in S but S is not contained in R
  • 21. Which relation is an example of the intersection of 'is a lower card than' and 'belongs to the same suit as'?
A) is a lower card of the same suit as
B) is maternal grandparent of
C) is parent of
D) is grandmother of
  • 22. Which relation is the composition of 'is mother of' and 'is parent of'?
A) is ancestor of
B) is grandmother of
C) is a lower card of the same suit as
D) is maternal grandparent of
  • 23. According to the text, is '4 < 4' true or false?
A) Depends on the set
B) Undefined
C) False
D) True
  • 24. What can be used to represent a relation on a finite set X?
A) A scalar value
B) A random list of numbers
C) A 3D-cube diagram
D) A directed graph
  • 25. Which representation is suitable for a relation on the infinite set of real numbers?
A) 2D-plot
B) Directed graph
C) Boolean matrix
D) Hasse diagram
  • 26. What is omitted in a Hasse diagram to simplify the image?
A) The bottom edge
B) The vertices
C) The labels
D) The arrows
  • 27. Which of the following is a reflexive relation?
A) is a divisor of
B) >
C) ≥
D) is a parent of
  • 28. An injective relation is also known as:
A) Right-total.
B) Left-total.
C) Right-unique.
D) Left-unique.
  • 29. A serial relation is also called:
A) Left-total.
B) Left-unique.
C) Right-total.
D) Right-unique.
  • 30. Every reflexive relation is also:
A) Serial.
B) Asymmetric.
C) Injective.
D) Irreflexive.
  • 31. A surjective relation is also known as:
A) Right-unique.
B) Right-total.
C) Left-total.
D) Left-unique.
  • 32. Which relation is an example of a serial relation over the integers?
A) is a blood relative of
B) is a parent of
C) is a divisor of
D) >
  • 33. A functional relation is also called:
A) A partial function.
B) A symmetric relation.
C) An injective relation.
D) A total relation.
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