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