MHB What is the relation between the sets A and B?

[normaldistribut]

Can anyone help explain this to me and solve this problem? I have gone over my textbook and I am having trouble understanding this. (Doh)

Find the domain, range, and when A=B, the diagraph of the relation R.
A={1,2,3,4,8}=B; a R b if and only if a|b.

A.Domain {1,2,3,4,8}
Range {1,4,6,9,15}
$\begin{bmatrix} 1 & 1 & 1 &1 \\ 0 & 1 & 1 &0 \\ 0 & 0 & 1 &1 \\ 0 & 1 & 0 &0 \\ 0 & 0 & 0 &0 \end{bmatrix}$

B.Domain {1,2,3,4}
Range {1,4,6,9}
$\begin{bmatrix} 1 & 1 & 1 &1 \\ 0 & 1 & 1 &0 \\ 0 & 0 & 1 &1 \\ 0 & 1 & 0 &0 \\ 0 & 0 & 0 &0 \end{bmatrix}$

C.Domain {1,2,3,4,5}
Range {1,4,6,7,9}
$\begin{bmatrix} 1 & 1 & 1 &1 \\ 0 & 1 & 1 &0 \\ 0 & 0 & 1 &1 \\ 0 & 1 & 0 &0 \\ 0 & 0 & 0 &0 \end{bmatrix}$

D.Domain {1,2,3,4,5}
Range {1,4,6,8,9}
$\begin{bmatrix} 1 & 1 & 1 &1 \\ 0 & 1 & 1 &0 \\ 0 & 0 & 1 &1 \\ 0 & 1 & 0 &0 \\ 0 & 0 & 0 &0 \end{bmatrix}$

 

[Evgeny.Makarov]

Find the domain, range, and when A=B, the diagraph of the relation R.

(1) Is "diagraph" supposed to be "digraph"?
(2) What is \f?
(3) What are A through D: answer variants or different problems?
(4) What are these matrices if the problem statement does not ask for them?

Also, please give the definitions of domain and range from your textbook

 

[normaldistribut]

Re: Digraph of the relation

1) I copied it directly from the problem given and it says diagraph, but it is supposed to be digraph.(Doh)
2) /f is something that when I created the matrices within text box, it added. It's not on the original problem though.
3)A-D are the four answer choices that they gave us for to choose from.
4) These matrices are part of the problem, this is why I was so confused when working this because it's not like what we had worked previously.

This is directly from the text:

"The domain of R, denoted by Dom(R), is the set of elements in A that are related to some element in B. In other words, Dom(R), a subset of A, is the set of all first elements in the pairs that make up R. Similarly, we define the range of R, denoted by Ran(R), to be the set of elements in B that are second elements of pairs in R, that is, all elements in B that are paired with some element in A.
Elements of A that are not in Dom(R) are not involved in the relation R in any way. This is also true for elements of B that are not in Ran(R)."

Thanks!

 

[Evgeny.Makarov]

Re: Digraph of the relation

2) /f is something that when I created the matrices within text box, it added. It's not on the original problem though.

It's "\f", not "/f". If you see the button "Edit post" under your post, then use it.

Similarly, we define the range of R, denoted by Ran(R), to be the set of elements in B that are second elements of pairs in R

In neither variant the suggested range is a subset of B = {1,2,3,4,8}. But then, if the proviso "A = {1,2,3,4,8} = B" pertains to the whole problem, why add "when A=B, [find] the diagraph of the relation R"? What I am saying is that the problem statement does not clearly define the sets on which the relation is defined. This causes doubt whether the relation is $a\mid b$ as well.

The matrices are probably adjacency matrices of this relation/digraph. However, it is not clear why they are not square matrices. Also, I can't see how a textbook can fail to describe representing graphs using matrices prior to giving this problem.

All in all, this problem is poorly stated. I would recommend learning the definitions of all concepts used here and then moving to similar problems.

 

[normaldistribut]

Re: Digraph of the relation

It's "\f", not "/f". If you see the button "Edit post" under your post, then use it.

Thank you for pointing that out and I'm sure that after your reminder, I'll remember that in future posts.

In neither variant the suggested range is a subset of B = {1,2,3,4,8}. But then, if the proviso "A = {1,2,3,4,8} = B" pertains to the whole problem, why add "when A=B, [find] the diagraph of the relation R"? What I am saying is that the problem statement does not clearly define the sets on which the relation is defined. This causes doubt whether the relation is $a\mid b$ as well.

The matrices are probably adjacency matrices of this relation/digraph. However, it is not clear why they are not square matrices. Also, I can't see how a textbook can fail to describe representing graphs using matrices prior to giving this problem.

All in all, this problem is poorly stated. I would recommend learning the definitions of all concepts used here and then moving to similar problems.

I learned the definitions and concepts of this particular subject this week and have worked similar problems. I didn't have a problem until I came across this one. That is why I looked to this board for help because clearly I'm not the only one that can't figure the problem out as well.

Thank you for taking the time to provide your response. (Handshake)

 

[I like Serena]

Re: Digraph of the relation

Hi normaldistribut! :)

With the information you provided, I took another look at the problem.

The answer is B.

We can find it by elimination, since it is the only one with an adjacency matrix that is (more or less) correctly defined.
Each row corresponds to an element from A={1,2,3,4,8}.
Each column corresponds to what is given as the range {1,4,6,9}.

Furthermore, 8 is the only element that does not divide any element in the range.
So the domain is indeed {1,2,3,4}.
Since each of these elements in the range can divided by an element in the domain, it is indeed the range.

Checking the adjacency matrix, shows that it matches the "divides by" operator.

 

[normaldistribut]

Thank you so much! After reading your reply and your instructions I see what I didn't do right and was able to figure out the second one that looked like this as well. YAY! Have an amazing day (Party)