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Question about equivalence relation that concludes C=D [closed]
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Here is a statement I retrieved from Munkres Topology. It states that for x in a set A
yCx if and only if yDx concludes that C=D. I don’t quite understand how this conclusion come from.
elementary-set-theory equivalence-relations
edited Jul 23 at 18:09
Andrés E. Caicedo
63.2k7151235
asked Jul 23 at 17:34
Ling Min Hao
31118
closed as unclear what you're asking by Andrés E. Caicedo, Mostafa Ayaz, Isaac Browne, Leucippus, Xander Henderson Jul 24 at 0:38
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |Â
up vote
0
down vote
favorite
Here is a statement I retrieved from Munkres Topology. It states that for x in a set A
yCx if and only if yDx concludes that C=D. I don’t quite understand how this conclusion come from.
elementary-set-theory equivalence-relations
edited Jul 23 at 18:09
Andrés E. Caicedo
63.2k7151235
asked Jul 23 at 17:34
Ling Min Hao
31118
closed as unclear what you're asking by Andrés E. Caicedo, Mostafa Ayaz, Isaac Browne, Leucippus, Xander Henderson Jul 24 at 0:38
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Do you know what a relation is, and, as a consequence, when two relations are equal?
– Adayah
Jul 23 at 17:36
I think two relations are equal if they have the same set of collection of ordered pair ?
– Ling Min Hao
Jul 23 at 17:38
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Here is a statement I retrieved from Munkres Topology. It states that for x in a set A
yCx if and only if yDx concludes that C=D. I don’t quite understand how this conclusion come from.
elementary-set-theory equivalence-relations
edited Jul 23 at 18:09
Andrés E. Caicedo
63.2k7151235
asked Jul 23 at 17:34
Ling Min Hao
31118
Here is a statement I retrieved from Munkres Topology. It states that for x in a set A
yCx if and only if yDx concludes that C=D. I don’t quite understand how this conclusion come from.
elementary-set-theory equivalence-relations
edited Jul 23 at 18:09
Andrés E. Caicedo
63.2k7151235
asked Jul 23 at 17:34
Ling Min Hao
31118
edited Jul 23 at 18:09
Andrés E. Caicedo
63.2k7151235
edited Jul 23 at 18:09
Andrés E. Caicedo
63.2k7151235
edited Jul 23 at 18:09
Andrés E. Caicedo
63.2k7151235
63.2k7151235
asked Jul 23 at 17:34
Ling Min Hao
31118
asked Jul 23 at 17:34
Ling Min Hao
31118
asked Jul 23 at 17:34
Ling Min Hao
31118
31118
closed as unclear what you're asking by Andrés E. Caicedo, Mostafa Ayaz, Isaac Browne, Leucippus, Xander Henderson Jul 24 at 0:38
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Andrés E. Caicedo, Mostafa Ayaz, Isaac Browne, Leucippus, Xander Henderson Jul 24 at 0:38
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Do you know what a relation is, and, as a consequence, when two relations are equal?
– Adayah
Jul 23 at 17:36
I think two relations are equal if they have the same set of collection of ordered pair ?
– Ling Min Hao
Jul 23 at 17:38
add a comment |Â
Do you know what a relation is, and, as a consequence, when two relations are equal?
– Adayah
Jul 23 at 17:36
I think two relations are equal if they have the same set of collection of ordered pair ?
– Ling Min Hao
Jul 23 at 17:38
Do you know what a relation is, and, as a consequence, when two relations are equal?
– Adayah
Jul 23 at 17:36
Do you know what a relation is, and, as a consequence, when two relations are equal?
– Adayah
Jul 23 at 17:36
I think two relations are equal if they have the same set of collection of ordered pair ?
– Ling Min Hao
Jul 23 at 17:38
I think two relations are equal if they have the same set of collection of ordered pair ?
– Ling Min Hao
Jul 23 at 17:38
add a comment |Â
1 Answer
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From the context, I am guessing that $C$ and $D$ are relations on the same set $A$. The formal definition of relation is a set of ordered pairs. So both $C$ and $D$ are subsets of $A times A$.
The syntactic sugar notation for a relation $Rsubseteq A times A$ is to write $x mathrelR y$ when $(x,y) in R$. So the statement $y mathrelC x iff y mathrelD x$ is syntactically equivalent to $(y,x) in C iff (y,x) in D$. But this is equivalent to $C = D$ as sets.
answered Jul 23 at 17:52
Matthew Leingang
15k12143
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
From the context, I am guessing that $C$ and $D$ are relations on the same set $A$. The formal definition of relation is a set of ordered pairs. So both $C$ and $D$ are subsets of $A times A$.
The syntactic sugar notation for a relation $Rsubseteq A times A$ is to write $x mathrelR y$ when $(x,y) in R$. So the statement $y mathrelC x iff y mathrelD x$ is syntactically equivalent to $(y,x) in C iff (y,x) in D$. But this is equivalent to $C = D$ as sets.
answered Jul 23 at 17:52
Matthew Leingang
15k12143
add a comment |Â
up vote
1
down vote
accepted
From the context, I am guessing that $C$ and $D$ are relations on the same set $A$. The formal definition of relation is a set of ordered pairs. So both $C$ and $D$ are subsets of $A times A$.
The syntactic sugar notation for a relation $Rsubseteq A times A$ is to write $x mathrelR y$ when $(x,y) in R$. So the statement $y mathrelC x iff y mathrelD x$ is syntactically equivalent to $(y,x) in C iff (y,x) in D$. But this is equivalent to $C = D$ as sets.
answered Jul 23 at 17:52
Matthew Leingang
15k12143
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
From the context, I am guessing that $C$ and $D$ are relations on the same set $A$. The formal definition of relation is a set of ordered pairs. So both $C$ and $D$ are subsets of $A times A$.
The syntactic sugar notation for a relation $Rsubseteq A times A$ is to write $x mathrelR y$ when $(x,y) in R$. So the statement $y mathrelC x iff y mathrelD x$ is syntactically equivalent to $(y,x) in C iff (y,x) in D$. But this is equivalent to $C = D$ as sets.
answered Jul 23 at 17:52
Matthew Leingang
15k12143
From the context, I am guessing that $C$ and $D$ are relations on the same set $A$. The formal definition of relation is a set of ordered pairs. So both $C$ and $D$ are subsets of $A times A$.
The syntactic sugar notation for a relation $Rsubseteq A times A$ is to write $x mathrelR y$ when $(x,y) in R$. So the statement $y mathrelC x iff y mathrelD x$ is syntactically equivalent to $(y,x) in C iff (y,x) in D$. But this is equivalent to $C = D$ as sets.
answered Jul 23 at 17:52
Matthew Leingang
15k12143
answered Jul 23 at 17:52
Matthew Leingang
15k12143
answered Jul 23 at 17:52
Matthew Leingang
15k12143
answered Jul 23 at 17:52
Matthew Leingang
15k12143
15k12143
add a comment |Â
add a comment |Â
Do you know what a relation is, and, as a consequence, when two relations are equal?
– Adayah
Jul 23 at 17:36
I think two relations are equal if they have the same set of collection of ordered pair ?
– Ling Min Hao
Jul 23 at 17:38