imo class 12 relations and functions

The empty relation on a non-empty set A is:

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#IMO#Class 12#Mathematics#Relations and Functions#logical-reasoning

The empty relation on a non-empty set A is:

  • A. Reflexive and symmetric
  • B. Symmetric and transitive
  • C. Reflexive and transitive
  • D. Equivalence

Answer: B) Symmetric and transitive

Explanation: The empty relation has no pairs. It is vacuously symmetric and transitive. However, since the set A is non-empty, it lacks (a,a) for elements in A, so it is not reflexive.

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