How would I draw the diagram for this relation?
$begingroup$
The question I am trying to solve is below. I have proven it is an order but am unsure how to draw the diagram for it. Can someone point me in the right direction?
Let A = {1, 2, 3, 4}, and let R be a binary relation on A × A given by: ((a, b),(c, d)) ∈ R if and only if a divides c and b divides d.
What I have so far, on the right track?
second level: (1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)(4,1)(4,2)(4,3)(4,4)
bottom level: (1,1)
discrete-mathematics relations
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
$endgroup$
add a comment |
$begingroup$
The question I am trying to solve is below. I have proven it is an order but am unsure how to draw the diagram for it. Can someone point me in the right direction?
Let A = {1, 2, 3, 4}, and let R be a binary relation on A × A given by: ((a, b),(c, d)) ∈ R if and only if a divides c and b divides d.
What I have so far, on the right track?
second level: (1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)(4,1)(4,2)(4,3)(4,4)
bottom level: (1,1)
discrete-mathematics relations
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
$endgroup$
$begingroup$
In the second level just write $(1,2),(1,3),(2,1)$ and $(3,1).$ Don't write $(2,2),$ for example, since you have $(1,2)$ and $(2,1)$ in the middle.
$endgroup$
– mfl
Oct 18 '14 at 23:16
add a comment |
$begingroup$
The question I am trying to solve is below. I have proven it is an order but am unsure how to draw the diagram for it. Can someone point me in the right direction?
Let A = {1, 2, 3, 4}, and let R be a binary relation on A × A given by: ((a, b),(c, d)) ∈ R if and only if a divides c and b divides d.
What I have so far, on the right track?
second level: (1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)(4,1)(4,2)(4,3)(4,4)
bottom level: (1,1)
discrete-mathematics relations
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
$endgroup$
The question I am trying to solve is below. I have proven it is an order but am unsure how to draw the diagram for it. Can someone point me in the right direction?
Let A = {1, 2, 3, 4}, and let R be a binary relation on A × A given by: ((a, b),(c, d)) ∈ R if and only if a divides c and b divides d.
What I have so far, on the right track?
second level: (1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)(4,1)(4,2)(4,3)(4,4)
bottom level: (1,1)
discrete-mathematics relations
discrete-mathematics relations
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
asked Oct 18 '14 at 22:23
user3362196user3362196
124210
124210
$begingroup$
In the second level just write $(1,2),(1,3),(2,1)$ and $(3,1).$ Don't write $(2,2),$ for example, since you have $(1,2)$ and $(2,1)$ in the middle.
$endgroup$
– mfl
Oct 18 '14 at 23:16
add a comment |
$begingroup$
In the second level just write $(1,2),(1,3),(2,1)$ and $(3,1).$ Don't write $(2,2),$ for example, since you have $(1,2)$ and $(2,1)$ in the middle.
$endgroup$
– mfl
Oct 18 '14 at 23:16
$begingroup$
In the second level just write $(1,2),(1,3),(2,1)$ and $(3,1).$ Don't write $(2,2),$ for example, since you have $(1,2)$ and $(2,1)$ in the middle.
$endgroup$
– mfl
Oct 18 '14 at 23:16
$begingroup$
In the second level just write $(1,2),(1,3),(2,1)$ and $(3,1).$ Don't write $(2,2),$ for example, since you have $(1,2)$ and $(2,1)$ in the middle.
$endgroup$
– mfl
Oct 18 '14 at 23:16
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
As was noted in the comments, you have far too much in your second level. For instance, $2mid 4$ and $1mid 1$, so $langle 2,1rangle$ must be below $langle 4,1rangle$. On the other hand, we know that there’s nothing between them, because there is no integer $n{1,2,3,4}$ such that $2mid n$, $nmid 4$, and $n$ is neither $2$ nor $4$.
Here are the bottom three levels; can you finish it from here?
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
$endgroup$
$begingroup$
Thanks I see it now! I can solve it from here :)
$endgroup$
– user3362196
Oct 19 '14 at 2:43
$begingroup$
@user3362196: You’re welcome!
$endgroup$
– Brian M. Scott
Oct 19 '14 at 2:45
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f980083%2fhow-would-i-draw-the-diagram-for-this-relation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
As was noted in the comments, you have far too much in your second level. For instance, $2mid 4$ and $1mid 1$, so $langle 2,1rangle$ must be below $langle 4,1rangle$. On the other hand, we know that there’s nothing between them, because there is no integer $n{1,2,3,4}$ such that $2mid n$, $nmid 4$, and $n$ is neither $2$ nor $4$.
Here are the bottom three levels; can you finish it from here?
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
$endgroup$
$begingroup$
Thanks I see it now! I can solve it from here :)
$endgroup$
– user3362196
Oct 19 '14 at 2:43
$begingroup$
@user3362196: You’re welcome!
$endgroup$
– Brian M. Scott
Oct 19 '14 at 2:45
add a comment |
$begingroup$
As was noted in the comments, you have far too much in your second level. For instance, $2mid 4$ and $1mid 1$, so $langle 2,1rangle$ must be below $langle 4,1rangle$. On the other hand, we know that there’s nothing between them, because there is no integer $n{1,2,3,4}$ such that $2mid n$, $nmid 4$, and $n$ is neither $2$ nor $4$.
Here are the bottom three levels; can you finish it from here?
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
$endgroup$
$begingroup$
Thanks I see it now! I can solve it from here :)
$endgroup$
– user3362196
Oct 19 '14 at 2:43
$begingroup$
@user3362196: You’re welcome!
$endgroup$
– Brian M. Scott
Oct 19 '14 at 2:45
add a comment |
$begingroup$
As was noted in the comments, you have far too much in your second level. For instance, $2mid 4$ and $1mid 1$, so $langle 2,1rangle$ must be below $langle 4,1rangle$. On the other hand, we know that there’s nothing between them, because there is no integer $n{1,2,3,4}$ such that $2mid n$, $nmid 4$, and $n$ is neither $2$ nor $4$.
Here are the bottom three levels; can you finish it from here?
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
$endgroup$
As was noted in the comments, you have far too much in your second level. For instance, $2mid 4$ and $1mid 1$, so $langle 2,1rangle$ must be below $langle 4,1rangle$. On the other hand, we know that there’s nothing between them, because there is no integer $n{1,2,3,4}$ such that $2mid n$, $nmid 4$, and $n$ is neither $2$ nor $4$.
Here are the bottom three levels; can you finish it from here?
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
answered Oct 19 '14 at 2:36
Brian M. ScottBrian M. Scott
461k40518921
461k40518921
$begingroup$
Thanks I see it now! I can solve it from here :)
$endgroup$
– user3362196
Oct 19 '14 at 2:43
$begingroup$
@user3362196: You’re welcome!
$endgroup$
– Brian M. Scott
Oct 19 '14 at 2:45
add a comment |
$begingroup$
Thanks I see it now! I can solve it from here :)
$endgroup$
– user3362196
Oct 19 '14 at 2:43
$begingroup$
@user3362196: You’re welcome!
$endgroup$
– Brian M. Scott
Oct 19 '14 at 2:45
$begingroup$
Thanks I see it now! I can solve it from here :)
$endgroup$
– user3362196
Oct 19 '14 at 2:43
$begingroup$
Thanks I see it now! I can solve it from here :)
$endgroup$
– user3362196
Oct 19 '14 at 2:43
$begingroup$
@user3362196: You’re welcome!
$endgroup$
– Brian M. Scott
Oct 19 '14 at 2:45
$begingroup$
@user3362196: You’re welcome!
$endgroup$
– Brian M. Scott
Oct 19 '14 at 2:45
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f980083%2fhow-would-i-draw-the-diagram-for-this-relation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
In the second level just write $(1,2),(1,3),(2,1)$ and $(3,1).$ Don't write $(2,2),$ for example, since you have $(1,2)$ and $(2,1)$ in the middle.
$endgroup$
– mfl
Oct 18 '14 at 23:16