Practice question · Multiple choice
An equivalence relation is said to partition a set into disjoint classes. What structural consequence follows when two elements share a single equivalence class?
Hints
- What does transitivity and symmetry force upon elements inside the same cell of a partition?
- Does being equivalent under a specific relation mean two elements are literally the same object?
Show the answer
B. They share identical relation pairs with every element across the domain
Why
Belonging to the same equivalence class means two elements are mutually related and share identical relational behaviour across the partition. It does not mean they are identical objects, nor does it force relations with external elements outside their class.
Practise Relations, Functions and Power Sets
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