# Relationship table

• Dec 12th 2011, 01:04 PM
nomanslan
Relationship table
Hi,
I have a question that is as follows:

"draw a talbe to show weather the following relations demostrate the following properties: symmetry, anti-symmetry, reflexivity, partial order, equivalence
a. differs by multiple 5
b. exaclty divides
c. is a permutation of"

all i can think of for
a: reflexivity, partial order,symmetry
b: symmetry,reflexivity
c: anti-symmetry,equivalence

but im not to sure im on the right path. can someone set me straight

thanks
• Dec 12th 2011, 01:49 PM
Plato
Re: Relationship table
Quote:

Originally Posted by nomanslan
"draw a talbe to show weather the following relations demostrate the following properties: symmetry, anti-symmetry, reflexivity, partial order, equivalence
a. differs by multiple 5
b. exaclty divides
c. is a permutation of"

There are several problems with this question.
You failed to tell us what set these relations are defined upon.
It appears that it may some subset of the integers.

In any case what in the world can "permutation of" mean as a relation?
• Dec 12th 2011, 02:02 PM
nomanslan
Re: Relationship table
it says after c. "(e.g 1,2,3,4 is a permutaion of 1,3,4,2)"

the question doesnt give me any integers to work with. thats all there is to the question
• Dec 12th 2011, 02:17 PM
Plato
Re: Relationship table
Quote:

Originally Posted by nomanslan
it says after c. "(e.g 1,2,3,4 is a permutaion of 1,3,4,2)" the question doesnt give me any integers to work with. thats all there is to the question

Well then, you have not been given enough information to answer any part of the question.
• Dec 13th 2011, 12:48 AM
emakarov
Re: Relationship table
As Plato said, the answers to some of the questions depend on the set A on which these relations are given. I'll assume that $A\subseteq\mathbb{Z}$, $A\ne\emptyset$ for (a) and (b) and $A\subseteq\mathbb{Z}^n$, $A\ne\emptyset$ for some n for (c).

Quote:

Originally Posted by nomanslan
"draw a talbe to show weather the following relations demostrate the following properties: symmetry, anti-symmetry, reflexivity, partial order, equivalence
a. differs by multiple 5
b. exaclty divides
c. is a permutation of"

all i can think of for
a: reflexivity, partial order,symmetry

If you list partial order, then you should list antisymmetry as well. In fact, antisymmetry and partial order only hold for some A. Reflexivity and symmetry are correct. This is an equivalence relation.

Quote:

Originally Posted by nomanslan
b: symmetry,reflexivity

Symmetry, antisymmetry, partial order and equivalence relation hold only for some A, reflexivity is correct.

Quote:

Originally Posted by nomanslan
c: anti-symmetry,equivalence

Antisymmetry and partial order hold for some A, symmetry, reflexivity and equivalence relation always.