Mixing
reflexive, symmetric, transitive and antisymmetric.
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
Can there be a relation which is reflexive, symmetric, transitive and antisymmetric at the same time?. I tried to find so .
If $A$ = a,b,c. Let $R$ be a relation which is reflexive, symmetric, transitive and antisymmetric.
$R$ = (a,a),(b,b),(c,c)
Is this correct? If im wrong can you help me understand it?
Since if (a,b) , (b,c) are elements of $R$ by transitive there would be (a,c) but then there should be (b,a) , (c , b) and (c,a) by symmetric but then it would not be anti symmetric. If im not mistaken.
relations symmetric-functions
asked 30 mins ago
Shehan Tearz
334
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
1
down vote
favorite
Can there be a relation which is reflexive, symmetric, transitive and antisymmetric at the same time?. I tried to find so .
If $A$ = a,b,c. Let $R$ be a relation which is reflexive, symmetric, transitive and antisymmetric.
$R$ = (a,a),(b,b),(c,c)
Is this correct? If im wrong can you help me understand it?
Since if (a,b) , (b,c) are elements of $R$ by transitive there would be (a,c) but then there should be (b,a) , (c , b) and (c,a) by symmetric but then it would not be anti symmetric. If im not mistaken.
relations symmetric-functions
asked 30 mins ago
Shehan Tearz
334
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Rather than simply telling you if you're right or where you're wrong, I would recommend you check methodically so you can be confident in the answer. To test transitivity, if you're concerned about missing something, you can write down all 9 pairs of elements or $R$ and see if they're of the form $(x,y)$ and $(y,z)$ (where some of $x,y,z$ can be the same) and if the corresponding $(x,z)$ is in $R$ too. For symmetry, look at all 3 elements of $R$. For reflectivity, look at all 3 elements of $A$. For antisymmetry, look at all 6 unordered pairs of elements of $R$ to look for $(x,y)$ and $(y,x)$.
– Mark S.
15 mins ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Can there be a relation which is reflexive, symmetric, transitive and antisymmetric at the same time?. I tried to find so .
If $A$ = a,b,c. Let $R$ be a relation which is reflexive, symmetric, transitive and antisymmetric.
$R$ = (a,a),(b,b),(c,c)
Is this correct? If im wrong can you help me understand it?
Since if (a,b) , (b,c) are elements of $R$ by transitive there would be (a,c) but then there should be (b,a) , (c , b) and (c,a) by symmetric but then it would not be anti symmetric. If im not mistaken.
relations symmetric-functions
asked 30 mins ago
Shehan Tearz
334
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Can there be a relation which is reflexive, symmetric, transitive and antisymmetric at the same time?. I tried to find so .
If $A$ = a,b,c. Let $R$ be a relation which is reflexive, symmetric, transitive and antisymmetric.
$R$ = (a,a),(b,b),(c,c)
Is this correct? If im wrong can you help me understand it?
Since if (a,b) , (b,c) are elements of $R$ by transitive there would be (a,c) but then there should be (b,a) , (c , b) and (c,a) by symmetric but then it would not be anti symmetric. If im not mistaken.
relations symmetric-functions
relations symmetric-functions
asked 30 mins ago
Shehan Tearz
334
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 30 mins ago
Shehan Tearz
334
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 30 mins ago
Shehan Tearz
334
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 30 mins ago
Shehan Tearz
334
asked 30 mins ago
Shehan Tearz
334
334
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Shehan Tearz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Rather than simply telling you if you're right or where you're wrong, I would recommend you check methodically so you can be confident in the answer. To test transitivity, if you're concerned about missing something, you can write down all 9 pairs of elements or $R$ and see if they're of the form $(x,y)$ and $(y,z)$ (where some of $x,y,z$ can be the same) and if the corresponding $(x,z)$ is in $R$ too. For symmetry, look at all 3 elements of $R$. For reflectivity, look at all 3 elements of $A$. For antisymmetry, look at all 6 unordered pairs of elements of $R$ to look for $(x,y)$ and $(y,x)$.
– Mark S.
15 mins ago
add a comment |Â
Rather than simply telling you if you're right or where you're wrong, I would recommend you check methodically so you can be confident in the answer. To test transitivity, if you're concerned about missing something, you can write down all 9 pairs of elements or $R$ and see if they're of the form $(x,y)$ and $(y,z)$ (where some of $x,y,z$ can be the same) and if the corresponding $(x,z)$ is in $R$ too. For symmetry, look at all 3 elements of $R$. For reflectivity, look at all 3 elements of $A$. For antisymmetry, look at all 6 unordered pairs of elements of $R$ to look for $(x,y)$ and $(y,x)$.
– Mark S.
15 mins ago
Rather than simply telling you if you're right or where you're wrong, I would recommend you check methodically so you can be confident in the answer. To test transitivity, if you're concerned about missing something, you can write down all 9 pairs of elements or $R$ and see if they're of the form $(x,y)$ and $(y,z)$ (where some of $x,y,z$ can be the same) and if the corresponding $(x,z)$ is in $R$ too. For symmetry, look at all 3 elements of $R$. For reflectivity, look at all 3 elements of $A$. For antisymmetry, look at all 6 unordered pairs of elements of $R$ to look for $(x,y)$ and $(y,x)$.
– Mark S.
15 mins ago
Rather than simply telling you if you're right or where you're wrong, I would recommend you check methodically so you can be confident in the answer. To test transitivity, if you're concerned about missing something, you can write down all 9 pairs of elements or $R$ and see if they're of the form $(x,y)$ and $(y,z)$ (where some of $x,y,z$ can be the same) and if the corresponding $(x,z)$ is in $R$ too. For symmetry, look at all 3 elements of $R$. For reflectivity, look at all 3 elements of $A$. For antisymmetry, look at all 6 unordered pairs of elements of $R$ to look for $(x,y)$ and $(y,x)$.
– Mark S.
15 mins ago
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
4
down vote
For any set $A$, there exists only one relation which is both reflexive, symmetric and assymetric, and that is the relation $R= ain A$.
You can easily see that any reflexive relation must include all elements of $A$, and that any relation that is symmetric and antisymmetric cannot include any pair $(a,b)$ where $aneq b$. So already, $R$ is your only candidate for a reflexive, symmetric, transitive and antisymmetric relation.
Since $R$ is also transitive, we conclude that $R$ is the only reflexive, symmetric, transitive and antisymmetric relation.
answered 27 mins ago
5xum
83.7k384148
add a comment |Â
up vote
1
down vote
Your answer is correct and you can easily generalize it to a set with more elements
Apparently the only solution to your question is the diagonal relation, $$R=(x,x)$$ for any set A.
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
For any set $A$, there exists only one relation which is both reflexive, symmetric and assymetric, and that is the relation $R= ain A$.
You can easily see that any reflexive relation must include all elements of $A$, and that any relation that is symmetric and antisymmetric cannot include any pair $(a,b)$ where $aneq b$. So already, $R$ is your only candidate for a reflexive, symmetric, transitive and antisymmetric relation.
Since $R$ is also transitive, we conclude that $R$ is the only reflexive, symmetric, transitive and antisymmetric relation.
answered 27 mins ago
5xum
83.7k384148
add a comment |Â
up vote
4
down vote
For any set $A$, there exists only one relation which is both reflexive, symmetric and assymetric, and that is the relation $R= ain A$.
You can easily see that any reflexive relation must include all elements of $A$, and that any relation that is symmetric and antisymmetric cannot include any pair $(a,b)$ where $aneq b$. So already, $R$ is your only candidate for a reflexive, symmetric, transitive and antisymmetric relation.
Since $R$ is also transitive, we conclude that $R$ is the only reflexive, symmetric, transitive and antisymmetric relation.
answered 27 mins ago
5xum
83.7k384148
add a comment |Â
up vote
4
down vote
up vote
4
down vote
For any set $A$, there exists only one relation which is both reflexive, symmetric and assymetric, and that is the relation $R= ain A$.
You can easily see that any reflexive relation must include all elements of $A$, and that any relation that is symmetric and antisymmetric cannot include any pair $(a,b)$ where $aneq b$. So already, $R$ is your only candidate for a reflexive, symmetric, transitive and antisymmetric relation.
Since $R$ is also transitive, we conclude that $R$ is the only reflexive, symmetric, transitive and antisymmetric relation.
answered 27 mins ago
5xum
83.7k384148
For any set $A$, there exists only one relation which is both reflexive, symmetric and assymetric, and that is the relation $R= ain A$.
You can easily see that any reflexive relation must include all elements of $A$, and that any relation that is symmetric and antisymmetric cannot include any pair $(a,b)$ where $aneq b$. So already, $R$ is your only candidate for a reflexive, symmetric, transitive and antisymmetric relation.
Since $R$ is also transitive, we conclude that $R$ is the only reflexive, symmetric, transitive and antisymmetric relation.
answered 27 mins ago
5xum
83.7k384148
answered 27 mins ago
5xum
83.7k384148
answered 27 mins ago
5xum
83.7k384148
answered 27 mins ago
5xum
83.7k384148
83.7k384148
add a comment |Â
add a comment |Â
up vote
1
down vote
Your answer is correct and you can easily generalize it to a set with more elements
Apparently the only solution to your question is the diagonal relation, $$R=(x,x)$$ for any set A.
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
add a comment |Â
up vote
1
down vote
Your answer is correct and you can easily generalize it to a set with more elements
Apparently the only solution to your question is the diagonal relation, $$R=(x,x)$$ for any set A.
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Your answer is correct and you can easily generalize it to a set with more elements
Apparently the only solution to your question is the diagonal relation, $$R=(x,x)$$ for any set A.
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
Your answer is correct and you can easily generalize it to a set with more elements
Apparently the only solution to your question is the diagonal relation, $$R=(x,x)$$ for any set A.
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
answered 20 mins ago
Mohammad Riazi-Kermani
32.3k41853
32.3k41853
add a comment |Â
add a comment |Â
Shehan Tearz is a new contributor. Be nice, and check out our Code of Conduct.
Shehan Tearz is a new contributor. Be nice, and check out our Code of Conduct.
Shehan Tearz is a new contributor. Be nice, and check out our Code of Conduct.
Shehan Tearz is a new contributor. Be nice, and check out our Code of Conduct.
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
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2930003%2freflexive-symmetric-transitive-and-antisymmetric%23new-answer', 'question_page');
);
Post as a guest
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
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
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
Rather than simply telling you if you're right or where you're wrong, I would recommend you check methodically so you can be confident in the answer. To test transitivity, if you're concerned about missing something, you can write down all 9 pairs of elements or $R$ and see if they're of the form $(x,y)$ and $(y,z)$ (where some of $x,y,z$ can be the same) and if the corresponding $(x,z)$ is in $R$ too. For symmetry, look at all 3 elements of $R$. For reflectivity, look at all 3 elements of $A$. For antisymmetry, look at all 6 unordered pairs of elements of $R$ to look for $(x,y)$ and $(y,x)$.
– Mark S.
15 mins ago