# Reflexivity, symmetry, and transitivity

Topology

Sets and Functions (XLVIII)

Functions

Decide which ones of the three properties of reflexivity, symmetry, and transitivity are true for each of the following relations in the set of all positive integers:

m is less than or equal to n, m < n, m divides n.

Are any of these equivalence relations?

See the attached file.

Â© BrainMass Inc. brainmass.com November 24, 2021, 1:11 pm ad1c9bdddfhttps://brainmass.com/math/geometry-and-topology/reflexivity-symmetry-transitivity-147745

#### Solution Preview

Topology

Sets and Functions (XLVIII)

Functions

Decide ...

#### Solution Summary

This solution is comprised of a detailed explanation of the properties of the equivalence relation.

It contains step-by-step explanation of the following problem:

Decide which ones of the three properties of reflexivity, symmetry, and transitivity are true for each of the following relations in the set of all positive integers:

m is less than or equal to n, m < n, m divides n.

Are any of these equivalence relations?