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Reflexivity, symmetry, and transitivity

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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.

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Topology
Sets and Functions (XLVIII)
Functions

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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?

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Reflexive, Symmetric, Transitive and Boolean products

1. Determine if the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) R if and only if x = 1.
a. reflexive
b. symmetric
c. antisymmetric
d. transitive

2. Find the Boolean product of the two matrices:
[ 0 1 0 ] [ 0 1 0 ]
[ 1 1 1 ] [ 0 1 1 ]
[ 1 0 0 ] [ 1 1 1 ]

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