Let be a binary relation defined on a non-empty set . Under which condition is classified as an equivalence relation?
Answer and explanation
Correct answer: A. is reflexive, symmetric, and transitive
- Step 1: By mathematical definition, a relation on set is an equivalence relation if and only if it satisfies three properties simultaneously.
- Step 2: It must be reflexive (), symmetric ($aRb \implies bRa$), and transitive ($aRb \land bRc \implies aRc$).
Answer
is reflexive, symmetric, and transitive.
Why not the others: Being only reflexive and symmetric does not ensure equivalence; omitting reflexivity violates self-relation; and antisymmetry characterizes partial orders.
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