Definition: Reflexivity can mean a property that applies to all or virtually all members of some set, whether it is a subset or not. A reflexive relation on a non-empty set A is a relation R in which every member x of A has an inverse (or converse) with respect to R. In other words, for each element y of A there exists at least one element x of A such that xRy. For example, consider the set A = {1, 2, 3}. The reflexive relation R on A is defined as follows: - Reflexivity: For all x in A, xRx. - Symmetry (or Transitivity): For all x, y and z in A with xRy and yRz, then xZ(zRy). - Antisymmetry (or Inversion): For all x, y and z in A with xRx and yRz, then x = y. The reflexive relation on the set A of 3 natural numbers is defined as follows: - Reflexivity: For any natural number n in A, there exists exactly one natural number m such that nm. - Symmetry (or Transitivity): For any natural number n, m and p in A with nm and mp, then n = mp. - Antisymmetry (or Inversion): For any natural number n, m and p in A with nm and pm, then n = mp. In other words, the reflexive property says that every member of a set has an inverse. You can also say that a reflexive relation is one where all elements are themselves reflections of each other.

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