Practice question · Select all that apply
Which are true of an equivalence relation?
Hints
- Three follow from the definition; one describes an ordering instead.
- Ordering requires asymmetry, which equivalence relations do not have.
Show the answer
- A. It partitions the set into disjoint classes
- B. It is reflexive
- C. It is symmetric
Why
An equivalence relation is reflexive, symmetric and transitive, and it carves the set into disjoint classes. Ordering needs anti-symmetry, which is incompatible with the symmetry an equivalence relation has.
Practise Relations, Functions and Power Sets
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