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