Question about Set Relations [on hold]Relations and transitivity.Relations on a set, check my...
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Question about Set Relations [on hold]
Relations and transitivity.Relations on a set, check my answers?Transitivity in set relationsDiscrete Maths Relations on the set {1,2,3,4}A simple conceptual doubt related to sets and relationsGiven set A, is the relation A x A always anti symmetric?R and S are equivalence relations on set A. Prove $Rcap S$ is an equivalence relation on A.Partial Order Relation and Equivalence RelationsFour Relations on ${1,2,3}$Identifying Equivalence Relations - Foundations of Mathematics
$begingroup$
Is A = {(1,1)} and B = {(2,2)}
then would A intersection B symmetric?
Also, which one is true
A intersection B = {NULL} OR,
A intersection B = NULL
relations
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
$endgroup$
put on hold as off-topic by Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song
If this question can be reworded to fit the rules in the help center, please edit the question.
|
show 2 more comments
$begingroup$
Is A = {(1,1)} and B = {(2,2)}
then would A intersection B symmetric?
Also, which one is true
A intersection B = {NULL} OR,
A intersection B = NULL
relations
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
$endgroup$
put on hold as off-topic by Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
I suspect you intend to have $A$ be a relation $A={(1,1)}$ instead if you are talking about symmetry. In either case $Acap B=emptyset$ and when interpreted as the empty relation is indeed symmetric. Note, $emptyset$ is different than ${emptyset}$
$endgroup$
– JMoravitz
Mar 9 at 17:42
$begingroup$
Thanks for the response.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
$begingroup$
Also, why an empty set is not reflexive. I read that somewhere.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
1
$begingroup$
A relation $S$ over a set $X$ is reflexive iff for every $xin X$ you have $(x,x)in S$... so long as $X$ is nonempty it should be painfully obvious that the empty set doesn't contain any such pairs, much less all such pairs which would be required to call it reflexive. (it actually is reflexive in the specific case where X happened to be empty as well, so the question was ill-formed)
$endgroup$
– JMoravitz
Mar 9 at 17:54
$begingroup$
It would be correct to say that a relation S, such that S is an empty set over an empty set, is Reflexive?
$endgroup$
– Sachin Chaudhary
Mar 9 at 18:02
|
show 2 more comments
$begingroup$
Is A = {(1,1)} and B = {(2,2)}
then would A intersection B symmetric?
Also, which one is true
A intersection B = {NULL} OR,
A intersection B = NULL
relations
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
$endgroup$
Is A = {(1,1)} and B = {(2,2)}
then would A intersection B symmetric?
Also, which one is true
A intersection B = {NULL} OR,
A intersection B = NULL
relations
relations
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
edited Mar 9 at 22:28
Andrés E. Caicedo
65.7k8160250
65.7k8160250
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
asked Mar 9 at 17:28
Sachin ChaudharySachin Chaudhary
205
205
put on hold as off-topic by Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Andrés E. Caicedo, Alex Provost, Shailesh, Thomas Shelby, Song
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
I suspect you intend to have $A$ be a relation $A={(1,1)}$ instead if you are talking about symmetry. In either case $Acap B=emptyset$ and when interpreted as the empty relation is indeed symmetric. Note, $emptyset$ is different than ${emptyset}$
$endgroup$
– JMoravitz
Mar 9 at 17:42
$begingroup$
Thanks for the response.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
$begingroup$
Also, why an empty set is not reflexive. I read that somewhere.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
1
$begingroup$
A relation $S$ over a set $X$ is reflexive iff for every $xin X$ you have $(x,x)in S$... so long as $X$ is nonempty it should be painfully obvious that the empty set doesn't contain any such pairs, much less all such pairs which would be required to call it reflexive. (it actually is reflexive in the specific case where X happened to be empty as well, so the question was ill-formed)
$endgroup$
– JMoravitz
Mar 9 at 17:54
$begingroup$
It would be correct to say that a relation S, such that S is an empty set over an empty set, is Reflexive?
$endgroup$
– Sachin Chaudhary
Mar 9 at 18:02
|
show 2 more comments
1
$begingroup$
I suspect you intend to have $A$ be a relation $A={(1,1)}$ instead if you are talking about symmetry. In either case $Acap B=emptyset$ and when interpreted as the empty relation is indeed symmetric. Note, $emptyset$ is different than ${emptyset}$
$endgroup$
– JMoravitz
Mar 9 at 17:42
$begingroup$
Thanks for the response.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
$begingroup$
Also, why an empty set is not reflexive. I read that somewhere.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
1
$begingroup$
A relation $S$ over a set $X$ is reflexive iff for every $xin X$ you have $(x,x)in S$... so long as $X$ is nonempty it should be painfully obvious that the empty set doesn't contain any such pairs, much less all such pairs which would be required to call it reflexive. (it actually is reflexive in the specific case where X happened to be empty as well, so the question was ill-formed)
$endgroup$
– JMoravitz
Mar 9 at 17:54
$begingroup$
It would be correct to say that a relation S, such that S is an empty set over an empty set, is Reflexive?
$endgroup$
– Sachin Chaudhary
Mar 9 at 18:02
1
1
$begingroup$
I suspect you intend to have $A$ be a relation $A={(1,1)}$ instead if you are talking about symmetry. In either case $Acap B=emptyset$ and when interpreted as the empty relation is indeed symmetric. Note, $emptyset$ is different than ${emptyset}$
$endgroup$
– JMoravitz
Mar 9 at 17:42
$begingroup$
I suspect you intend to have $A$ be a relation $A={(1,1)}$ instead if you are talking about symmetry. In either case $Acap B=emptyset$ and when interpreted as the empty relation is indeed symmetric. Note, $emptyset$ is different than ${emptyset}$
$endgroup$
– JMoravitz
Mar 9 at 17:42
$begingroup$
Thanks for the response.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
$begingroup$
Thanks for the response.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
$begingroup$
Also, why an empty set is not reflexive. I read that somewhere.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
$begingroup$
Also, why an empty set is not reflexive. I read that somewhere.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
1
1
$begingroup$
A relation $S$ over a set $X$ is reflexive iff for every $xin X$ you have $(x,x)in S$... so long as $X$ is nonempty it should be painfully obvious that the empty set doesn't contain any such pairs, much less all such pairs which would be required to call it reflexive. (it actually is reflexive in the specific case where X happened to be empty as well, so the question was ill-formed)
$endgroup$
– JMoravitz
Mar 9 at 17:54
$begingroup$
A relation $S$ over a set $X$ is reflexive iff for every $xin X$ you have $(x,x)in S$... so long as $X$ is nonempty it should be painfully obvious that the empty set doesn't contain any such pairs, much less all such pairs which would be required to call it reflexive. (it actually is reflexive in the specific case where X happened to be empty as well, so the question was ill-formed)
$endgroup$
– JMoravitz
Mar 9 at 17:54
$begingroup$
It would be correct to say that a relation S, such that S is an empty set over an empty set, is Reflexive?
$endgroup$
– Sachin Chaudhary
Mar 9 at 18:02
$begingroup$
It would be correct to say that a relation S, such that S is an empty set over an empty set, is Reflexive?
$endgroup$
– Sachin Chaudhary
Mar 9 at 18:02
|
show 2 more comments
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$begingroup$
I suspect you intend to have $A$ be a relation $A={(1,1)}$ instead if you are talking about symmetry. In either case $Acap B=emptyset$ and when interpreted as the empty relation is indeed symmetric. Note, $emptyset$ is different than ${emptyset}$
$endgroup$
– JMoravitz
Mar 9 at 17:42
$begingroup$
Thanks for the response.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
$begingroup$
Also, why an empty set is not reflexive. I read that somewhere.
$endgroup$
– Sachin Chaudhary
Mar 9 at 17:49
1
$begingroup$
A relation $S$ over a set $X$ is reflexive iff for every $xin X$ you have $(x,x)in S$... so long as $X$ is nonempty it should be painfully obvious that the empty set doesn't contain any such pairs, much less all such pairs which would be required to call it reflexive. (it actually is reflexive in the specific case where X happened to be empty as well, so the question was ill-formed)
$endgroup$
– JMoravitz
Mar 9 at 17:54
$begingroup$
It would be correct to say that a relation S, such that S is an empty set over an empty set, is Reflexive?
$endgroup$
– Sachin Chaudhary
Mar 9 at 18:02