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The chapter discusses various properties of equivalence relations and their interactions, particularly focusing on unions and intersections of these relations. It explores how unions may fail to maintain transitivity while intersections consistently result in equivalence relations. Additionally, the chapter covers the counting of partitions in sets and the conditions under which a poset can be classified as a total order.
Chapter 111 sections
The chapter discusses various properties of equivalence relations and their interactions, particularly focusing on unions and intersections of these relations. It explores how unions may fail to maintain transitivity while intersections consistently result in equivalence relations. Additionally, the chapter covers the counting of partitions in sets and the conditions under which a poset can be classified as a total order.
The union of two equivalence relations is always reflexive and symmetric but may not be transitive.
The intersection of two equivalence relations is always an equivalence relation.
Every equivalence relation corresponds to a unique partition of a set.
A relation that is reflexive, symmetric, and transitive.
Combining two relations where the resulting relation retains reflexivity and symmetry but not necessarily transitivity.
The set of pairs that are in both relations, which will always form an equivalence relation if both are equivalence relations.
A set combined with a relation that is reflexive, antisymmetric, and transitive.
A poset where every pair of elements is comparable.
Total Questions
2
Estimated Time
4 min
Passing Score
70%
1 more question available