Let “x1 is a clone of x” mean that x1 is identical to x in all physical…
2010
Let “x1 is a clone of x” mean that x1 is identical to x in all physical attributes—height, weight, and complexion. Assume that these three attributes form the complete set of attributes for an entity. Under this definition, cloning is an equivalence relation. What is your assessment of this statement?
Answer: A. The statement is true — ConceptAn equivalence relation is a binary relation that is reflexive, symmetric, and transitive. If each entity is represented by a complete attribute tuple…
- A.
The statement is true
- B.
The statement is false
- C.
The truth value of the statement cannot be determined
- D.
The relation is symmetric and transitive, but not reflexive
Attempted by 26 students.
Show answer & explanation
Correct answer: A
Concept
An equivalence relation is a binary relation that is reflexive, symmetric, and transitive.
If each entity is represented by a complete attribute tuple f(x), then defining x R y exactly when f(x) = f(y) makes R equality on those tuples.
Application
Reflexive: For every entity x, f(x) = f(x), so x is related to itself.
Symmetric: If f(x1) = f(x), then f(x) = f(x1), so reversing the pair preserves the relation.
Transitive: If f(x1) = f(x) and f(x2) = f(x1), then f(x2) = f(x), so the relation passes through an intermediate entity.
Cross-check and contrast
“The statement is true” follows because equality of complete attribute tuples has all three equivalence properties.
“The statement is false” would require at least one of reflexivity, symmetry, or transitivity to fail, but none fails here.
“The truth value cannot be determined” does not apply because the complete attribute tuple and the relation are explicitly defined.
“The relation is symmetric and transitive, but not reflexive” overlooks that every entity has the same complete attribute tuple as itself.
Therefore, cloning under the stated definition is an equivalence relation, and the statement is true.