
Solving a Multi Part Matrix
This solution is enclosed within an attached pdf file which details how to work with various mathematical properties including reflexive relations, antisymmetric relations and transitive properties.

Determine reflexive, symmetric, antisymmetric, transitive, partial order and equivalence.
A partial order is a reflexive, antisymmetric, and
transitive relation. R has all three properties and
therefore is antisymmetric.
6.

Discrete mathematics
Partial order relation: Yes
From above, we know that D satisfies Reflexive, Transitive and Antisymmetric, then D is a partial order relation.
Total order relation: No
Because if x and y are brothers, then both x D y and y D x do not hold.

Binary Relations : Reflexive and Transitive, but not Antisymmetric
18402 Binary Relations : Reflexive and Transitive, but not Antisymmetric Give an example of or else prove that there are no relations on {a,b,c} that is reflexive and transitive, but not antisymmetric. Here is an example.
Suppose xRy means x^2=y^2.

Question about Relation  Ordered Pairs
(c) Is this relation a partial order? Explain. If this relation a partial order, draw its Hasse diagram.
(d) Use Warshall's Algorithm to determine the transitive closure of R. Note there are 2 versions of Washall's Algorithm.

A Discussion On Binary Relations : Reflexive, Symmetric, Antisymmetric, and/or Transitive
18401 A Discussion On Binary Relations : Reflexive, Symmetric, Antisymmetric, and/or Transitive Determine whether the binary relation R on Z, where aRb means a^2 = b^2, is reflexive, symmetric, antisymmetric, and/or transitive. aRb if and only if a^2=

Reflexive, Antisymmetric and Transitive Properties : Hasse Diagram and Boolean Matrix
Write the definitions of the properties, reflexive, antisymmetric and transitive and the use
the definitions to determine whether each property holds for this relation.
(a) Is this relation a partial ordering relation? Why?

Discrete Math  Definitions : Combinatorics, Enumeration, Permutation, Relation on A, Rn, Reflexive, Symmetric, Antisymmetric and Transitive
Transitive: R is said to be Transitive if (x,y), (y,z) are elements of R then (x,z) is an element of R. Definitions of Combinatorics, Enumeration, Permutation, Relation on A, Rn, Reflexive, Symmetric, Antisymmetric and Transitive are provided.

Steps on Solving Discrete Questions
The topics include Binomial Theorem, coefficient of terms, reflexive property, antisymmetric property, transitive property and partial order.