- What is a relation on a set?
- How many relations are there on a set with n elements?
- What is a reflexive relation?
- What is a symmetric relation?
- What is an antisymmetric relation?
- What is a transitive relation?
- Give an example of a relation on the set {1, 2, 3, 4} that is reflexive, symmetric, and not transitive.
- Give an example of a relation on the set {1, 2, 3, 4} that is not reflexive, symmetric, and transitive.
- Give an example of a relation on the set {1, 2, 3, 4} that is reflexive, antisymmetric, and not transitive.
- Give an example of a relation on the set {1, 2, 3, 4} that is reflexive, symmetric, and transitive.
- Give an example of a relation on the set {1, 2, 3, 4} that is reflexive, antisymmetric, and transitive.
- How many reflexive relations are there on a set with n elements?
- How many symmetric relations are there on a set with n elements?
- How many antisymmetric relations are there on a set with n elements?
- Explain how an n-ary relation can be used to represent information about students at a university.
- How can the 5-ary relation containing names of students, their addresses, telephone numbers, majors, and grade point averages be used to form a 3-ary relation containing the names of students, their majors, and their grade point averages?
- How can the 4-ary relation containing names of students, their addresses, telephone numbers, and majors, and the 4-ary relation containing names of students, their student numbers, majors, and numbers of credit hours be combined into a single n-ary relation?
- Explain how to use a zero-one matrix to represent a relation on a finite set.
- Explain how to use the zero-one matrix representing a relation to determine whether the relation is reflexive, symmetric, and/or antisymmetric.
- Explain how to use a directed graph to represent a relation on a finite set.
- Explain how to use the directed graph representing a relation to determine whether a relation is reflexive, symmetric, and/or antisymmetric.
- Define the reflexive closure and the symmetric closure of a relation.
- How can you construct the reflexive closure of a relation?
- How can you construct the symmetric closure of a relation?
- Find the reflexive closure and the symmetric closure of the relation {(1,2), (2,3), (2,4), (3,1)} on the set {1,2,3,4}.
- Define the transitive closure of a relation.
- Can the transitive closure of a relation be obtained by including all pairs (a, c) such that (a, b) and (b, c) belong to the relation?
- Describe two algorithms for finding the transitive closure of a relation.
- Find the transitive closure of the relation {(1, 1), (1, 3), (2, 1), (2, 3), (2, 4), (3, 2), (3, 4), (4, 1)}.
- Define an equivalence relation.
- Which relations on the set {a, b, c, d} are equivalence relations and contain (a, b) and (b, d)?
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