Which of the following is an equivalence relation?
Which of the following is an equivalence relation?
- A. R = {(a, b) : a > b} on R
- B. R = {(a, b) : a ≥ b} on R
- C. R = {(a, b) : a = b} on any set
- D. R = {(a, b) : a is the father of b} on the set of humans
Answer: C) R = {(a, b) : a = b} on any set
Explanation: a = b is reflexive, symmetric (if a = b then b = a), and transitive. 'Greater than' is not reflexive or symmetric. 'Greater than or equal to' is not symmetric. Father relation is not reflexive, symmetric, or transitive.
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