Why does this relation fail symmetry and transitivity properties?Properties of Relations. Reflexive,...
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Why does this relation fail symmetry and transitivity properties?
Properties of Relations. Reflexive, Symmetric, and Transitive.$beta$ as the relation “is a brother of”Smallest relation for reflexive, symmetry and transitivityProving Reflexivity, Symmetry and Transitivity of a RelationProving symmetry and transitivityWhy $yC_1x iff yC_2x$ implies $C_1 = C_2$? $C_i$ is a relation.Equivalence relation and partitions.Commutative pairs of relations do not define an equivalence relationProof of transitivity for equivalence relationDoes symmetry and transitivity imply reflexivity for nonempty binary relation?
$begingroup$
The question states, let $S$ be the set of all humans.
Define $a ∼ b$ iff $a$ is a full-brother
of $b$.
Symmetry: Since $a$ shares both parents with $b$, then $b$ shares both parents with $a$. Would this be false because $b$ is not defined as a male, so $b$ is instead the full sister of $a$?
Transitivity: Since $a$ shares both parents with $b$, and $b$ shares both parents with $c$, then a shares both parents with $c$. What does the $c$ mean in this context? Is it simply another person introduced?
discrete-mathematics relations equivalence-relations
asked 40 mins ago
Michael RamageMichael Ramage
234
$endgroup$
add a comment |
$begingroup$
The question states, let $S$ be the set of all humans.
Define $a ∼ b$ iff $a$ is a full-brother
of $b$.
Symmetry: Since $a$ shares both parents with $b$, then $b$ shares both parents with $a$. Would this be false because $b$ is not defined as a male, so $b$ is instead the full sister of $a$?
Transitivity: Since $a$ shares both parents with $b$, and $b$ shares both parents with $c$, then a shares both parents with $c$. What does the $c$ mean in this context? Is it simply another person introduced?
discrete-mathematics relations equivalence-relations
asked 40 mins ago
Michael RamageMichael Ramage
234
$endgroup$
add a comment |
$begingroup$
The question states, let $S$ be the set of all humans.
Define $a ∼ b$ iff $a$ is a full-brother
of $b$.
Symmetry: Since $a$ shares both parents with $b$, then $b$ shares both parents with $a$. Would this be false because $b$ is not defined as a male, so $b$ is instead the full sister of $a$?
Transitivity: Since $a$ shares both parents with $b$, and $b$ shares both parents with $c$, then a shares both parents with $c$. What does the $c$ mean in this context? Is it simply another person introduced?
discrete-mathematics relations equivalence-relations
asked 40 mins ago
Michael RamageMichael Ramage
234
$endgroup$
The question states, let $S$ be the set of all humans.
Define $a ∼ b$ iff $a$ is a full-brother
of $b$.
Symmetry: Since $a$ shares both parents with $b$, then $b$ shares both parents with $a$. Would this be false because $b$ is not defined as a male, so $b$ is instead the full sister of $a$?
Transitivity: Since $a$ shares both parents with $b$, and $b$ shares both parents with $c$, then a shares both parents with $c$. What does the $c$ mean in this context? Is it simply another person introduced?
discrete-mathematics relations equivalence-relations
discrete-mathematics relations equivalence-relations
asked 40 mins ago
Michael RamageMichael Ramage
234
asked 40 mins ago
Michael RamageMichael Ramage
234
edited 18 mins ago
Michael Ramage
asked 40 mins ago
Michael RamageMichael Ramage
234
asked 40 mins ago
Michael RamageMichael Ramage
234
asked 40 mins ago
Michael RamageMichael Ramage
234
234
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
For a relation to be equvalence relation you also need reflexivity that is
$$
asim a, qquad forall a in S.
$$
which would mean that $a$ is a full brother of himself which is absurd.
Reflecting on your other questions if you define $sim$ to be brothership then you definitely run into trouble with different sexes. So in case of $a$ and $b$ has different sex it is not holding up.
For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up.
I hope I could help
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
$endgroup$
$begingroup$
This helps. Thank you! I am trying to figure out why the back of the book states that all properties fail for this relation. Perhaps it is a type. I have seen a few along my journey through it.
$endgroup$
– Michael Ramage
26 mins ago
$begingroup$
" For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up" it fails if a and c are the same person.
$endgroup$
– fleablood
47 secs ago
add a comment |
$begingroup$
I am a full brother of my sister, but my sister is not a full brother of me. So this relation is not symmetric.
Transitivity is true though. If $a$ is a full brother of $b$ and $b$ is a full brother of $c$, then $a$ is a full brother of $c$.
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
$endgroup$
$begingroup$
... and yes, in this case $c$ is just a third person introduced.
$endgroup$
– Arthur
31 mins ago
$begingroup$
Since a is a full brother of b and b is a full brother of c means that both a and b are males, so c can be a sister to a and b. Even in that case, a is the brother of c. However, the back of my book says that all properties fail. I do not know if this is a type or not. Thank you both!
$endgroup$
– Michael Ramage
28 mins ago
$begingroup$
" Transitivity is true though. If a is a full brother of b and b is a full brother of c , then is a full brother of a". Not if a and c are the same person! Transitivity fails.
$endgroup$
– fleablood
3 mins ago
add a comment |
$begingroup$
Your title is inaccurate. An equivalence relationship can't fail symmetric and transitive properties, by definition, and this is not an equivalence relation because it does fail.
It fails reflexive because $a $~$a $ never happens. No-one is their own brother.
It fails symmetry for exactly the reason you state. If Allen, a boy, and Betty, girl, have the same parents than Allen is a full brother to Betty, but Betty is not a full brother to Allen.
Update!
Transitivity fails. If Allen is a full brother to Bob. And Bob is a full brother to Allen then Allen is not a full brother to Allen.
Transitivity fails.
===
I suppose we can define $a $~$b $ as 1) $a $ and be have the same parents, 2) $a $ is male, 3) $a $ and $b $ are different people.
Since no-one can 3) be a different person than oneself reflexivity can never happen. 2)Also being male may or may not occur. But 1) have same parents as self must always occur.
If $a $~$b $ then 1) $b$ and $a $ have same parents and 3) $b $
answered 19 mins ago
fleabloodfleablood
71.4k22686
$endgroup$
$begingroup$
I have corrected it. Does it read correct now?
$endgroup$
– Michael Ramage
17 mins ago
$begingroup$
Yes. it's a relation. But it's not an equivalence relation. It's not an equivalence relation because it fails. BTW I don't know why your book says transitivity fails.
$endgroup$
– fleablood
15 mins ago
$begingroup$
I understand. It is a book by my professor Alex McCallister, "A Transition to Advanced Mathematics: A Survey Course." I have spent several hours attempting to understand why transitivity fails, when it does not, unfortunately.
$endgroup$
– Michael Ramage
12 mins ago
$begingroup$
Got it! If $a$ and $b $ are both boys then $a=b$ and $b=a$ but $ane a$.
$endgroup$
– fleablood
4 mins ago
add a comment |
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3 Answers
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active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
For a relation to be equvalence relation you also need reflexivity that is
$$
asim a, qquad forall a in S.
$$
which would mean that $a$ is a full brother of himself which is absurd.
Reflecting on your other questions if you define $sim$ to be brothership then you definitely run into trouble with different sexes. So in case of $a$ and $b$ has different sex it is not holding up.
For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up.
I hope I could help
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
$endgroup$
$begingroup$
This helps. Thank you! I am trying to figure out why the back of the book states that all properties fail for this relation. Perhaps it is a type. I have seen a few along my journey through it.
$endgroup$
– Michael Ramage
26 mins ago
$begingroup$
" For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up" it fails if a and c are the same person.
$endgroup$
– fleablood
47 secs ago
add a comment |
$begingroup$
For a relation to be equvalence relation you also need reflexivity that is
$$
asim a, qquad forall a in S.
$$
which would mean that $a$ is a full brother of himself which is absurd.
Reflecting on your other questions if you define $sim$ to be brothership then you definitely run into trouble with different sexes. So in case of $a$ and $b$ has different sex it is not holding up.
For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up.
I hope I could help
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
$endgroup$
$begingroup$
This helps. Thank you! I am trying to figure out why the back of the book states that all properties fail for this relation. Perhaps it is a type. I have seen a few along my journey through it.
$endgroup$
– Michael Ramage
26 mins ago
$begingroup$
" For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up" it fails if a and c are the same person.
$endgroup$
– fleablood
47 secs ago
add a comment |
$begingroup$
For a relation to be equvalence relation you also need reflexivity that is
$$
asim a, qquad forall a in S.
$$
which would mean that $a$ is a full brother of himself which is absurd.
Reflecting on your other questions if you define $sim$ to be brothership then you definitely run into trouble with different sexes. So in case of $a$ and $b$ has different sex it is not holding up.
For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up.
I hope I could help
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
$endgroup$
For a relation to be equvalence relation you also need reflexivity that is
$$
asim a, qquad forall a in S.
$$
which would mean that $a$ is a full brother of himself which is absurd.
Reflecting on your other questions if you define $sim$ to be brothership then you definitely run into trouble with different sexes. So in case of $a$ and $b$ has different sex it is not holding up.
For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up.
I hope I could help
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
answered 29 mins ago
Vinyl_coat_jawaVinyl_coat_jawa
2,9651130
2,9651130
$begingroup$
This helps. Thank you! I am trying to figure out why the back of the book states that all properties fail for this relation. Perhaps it is a type. I have seen a few along my journey through it.
$endgroup$
– Michael Ramage
26 mins ago
$begingroup$
" For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up" it fails if a and c are the same person.
$endgroup$
– fleablood
47 secs ago
add a comment |
$begingroup$
This helps. Thank you! I am trying to figure out why the back of the book states that all properties fail for this relation. Perhaps it is a type. I have seen a few along my journey through it.
$endgroup$
– Michael Ramage
26 mins ago
$begingroup$
" For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up" it fails if a and c are the same person.
$endgroup$
– fleablood
47 secs ago
$begingroup$
This helps. Thank you! I am trying to figure out why the back of the book states that all properties fail for this relation. Perhaps it is a type. I have seen a few along my journey through it.
$endgroup$
– Michael Ramage
26 mins ago
$begingroup$
This helps. Thank you! I am trying to figure out why the back of the book states that all properties fail for this relation. Perhaps it is a type. I have seen a few along my journey through it.
$endgroup$
– Michael Ramage
26 mins ago
$begingroup$
" For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up" it fails if a and c are the same person.
$endgroup$
– fleablood
47 secs ago
$begingroup$
" For the question about transitivity you would read, "a is a full brother of b" and "b is a full brother of c". I would say that this holds up" it fails if a and c are the same person.
$endgroup$
– fleablood
47 secs ago
add a comment |
$begingroup$
I am a full brother of my sister, but my sister is not a full brother of me. So this relation is not symmetric.
Transitivity is true though. If $a$ is a full brother of $b$ and $b$ is a full brother of $c$, then $a$ is a full brother of $c$.
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
$endgroup$
$begingroup$
... and yes, in this case $c$ is just a third person introduced.
$endgroup$
– Arthur
31 mins ago
$begingroup$
Since a is a full brother of b and b is a full brother of c means that both a and b are males, so c can be a sister to a and b. Even in that case, a is the brother of c. However, the back of my book says that all properties fail. I do not know if this is a type or not. Thank you both!
$endgroup$
– Michael Ramage
28 mins ago
$begingroup$
" Transitivity is true though. If a is a full brother of b and b is a full brother of c , then is a full brother of a". Not if a and c are the same person! Transitivity fails.
$endgroup$
– fleablood
3 mins ago
add a comment |
$begingroup$
I am a full brother of my sister, but my sister is not a full brother of me. So this relation is not symmetric.
Transitivity is true though. If $a$ is a full brother of $b$ and $b$ is a full brother of $c$, then $a$ is a full brother of $c$.
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
$endgroup$
$begingroup$
... and yes, in this case $c$ is just a third person introduced.
$endgroup$
– Arthur
31 mins ago
$begingroup$
Since a is a full brother of b and b is a full brother of c means that both a and b are males, so c can be a sister to a and b. Even in that case, a is the brother of c. However, the back of my book says that all properties fail. I do not know if this is a type or not. Thank you both!
$endgroup$
– Michael Ramage
28 mins ago
$begingroup$
" Transitivity is true though. If a is a full brother of b and b is a full brother of c , then is a full brother of a". Not if a and c are the same person! Transitivity fails.
$endgroup$
– fleablood
3 mins ago
add a comment |
$begingroup$
I am a full brother of my sister, but my sister is not a full brother of me. So this relation is not symmetric.
Transitivity is true though. If $a$ is a full brother of $b$ and $b$ is a full brother of $c$, then $a$ is a full brother of $c$.
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
$endgroup$
I am a full brother of my sister, but my sister is not a full brother of me. So this relation is not symmetric.
Transitivity is true though. If $a$ is a full brother of $b$ and $b$ is a full brother of $c$, then $a$ is a full brother of $c$.
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
answered 32 mins ago
Robert IsraelRobert Israel
325k23214468
325k23214468
$begingroup$
... and yes, in this case $c$ is just a third person introduced.
$endgroup$
– Arthur
31 mins ago
$begingroup$
Since a is a full brother of b and b is a full brother of c means that both a and b are males, so c can be a sister to a and b. Even in that case, a is the brother of c. However, the back of my book says that all properties fail. I do not know if this is a type or not. Thank you both!
$endgroup$
– Michael Ramage
28 mins ago
$begingroup$
" Transitivity is true though. If a is a full brother of b and b is a full brother of c , then is a full brother of a". Not if a and c are the same person! Transitivity fails.
$endgroup$
– fleablood
3 mins ago
add a comment |
$begingroup$
... and yes, in this case $c$ is just a third person introduced.
$endgroup$
– Arthur
31 mins ago
$begingroup$
Since a is a full brother of b and b is a full brother of c means that both a and b are males, so c can be a sister to a and b. Even in that case, a is the brother of c. However, the back of my book says that all properties fail. I do not know if this is a type or not. Thank you both!
$endgroup$
– Michael Ramage
28 mins ago
$begingroup$
" Transitivity is true though. If a is a full brother of b and b is a full brother of c , then is a full brother of a". Not if a and c are the same person! Transitivity fails.
$endgroup$
– fleablood
3 mins ago
$begingroup$
... and yes, in this case $c$ is just a third person introduced.
$endgroup$
– Arthur
31 mins ago
$begingroup$
... and yes, in this case $c$ is just a third person introduced.
$endgroup$
– Arthur
31 mins ago
$begingroup$
Since a is a full brother of b and b is a full brother of c means that both a and b are males, so c can be a sister to a and b. Even in that case, a is the brother of c. However, the back of my book says that all properties fail. I do not know if this is a type or not. Thank you both!
$endgroup$
– Michael Ramage
28 mins ago
$begingroup$
Since a is a full brother of b and b is a full brother of c means that both a and b are males, so c can be a sister to a and b. Even in that case, a is the brother of c. However, the back of my book says that all properties fail. I do not know if this is a type or not. Thank you both!
$endgroup$
– Michael Ramage
28 mins ago
$begingroup$
" Transitivity is true though. If a is a full brother of b and b is a full brother of c , then is a full brother of a". Not if a and c are the same person! Transitivity fails.
$endgroup$
– fleablood
3 mins ago
$begingroup$
" Transitivity is true though. If a is a full brother of b and b is a full brother of c , then is a full brother of a". Not if a and c are the same person! Transitivity fails.
$endgroup$
– fleablood
3 mins ago
add a comment |
$begingroup$
Your title is inaccurate. An equivalence relationship can't fail symmetric and transitive properties, by definition, and this is not an equivalence relation because it does fail.
It fails reflexive because $a $~$a $ never happens. No-one is their own brother.
It fails symmetry for exactly the reason you state. If Allen, a boy, and Betty, girl, have the same parents than Allen is a full brother to Betty, but Betty is not a full brother to Allen.
Update!
Transitivity fails. If Allen is a full brother to Bob. And Bob is a full brother to Allen then Allen is not a full brother to Allen.
Transitivity fails.
===
I suppose we can define $a $~$b $ as 1) $a $ and be have the same parents, 2) $a $ is male, 3) $a $ and $b $ are different people.
Since no-one can 3) be a different person than oneself reflexivity can never happen. 2)Also being male may or may not occur. But 1) have same parents as self must always occur.
If $a $~$b $ then 1) $b$ and $a $ have same parents and 3) $b $
answered 19 mins ago
fleabloodfleablood
71.4k22686
$endgroup$
$begingroup$
I have corrected it. Does it read correct now?
$endgroup$
– Michael Ramage
17 mins ago
$begingroup$
Yes. it's a relation. But it's not an equivalence relation. It's not an equivalence relation because it fails. BTW I don't know why your book says transitivity fails.
$endgroup$
– fleablood
15 mins ago
$begingroup$
I understand. It is a book by my professor Alex McCallister, "A Transition to Advanced Mathematics: A Survey Course." I have spent several hours attempting to understand why transitivity fails, when it does not, unfortunately.
$endgroup$
– Michael Ramage
12 mins ago
$begingroup$
Got it! If $a$ and $b $ are both boys then $a=b$ and $b=a$ but $ane a$.
$endgroup$
– fleablood
4 mins ago
add a comment |
$begingroup$
Your title is inaccurate. An equivalence relationship can't fail symmetric and transitive properties, by definition, and this is not an equivalence relation because it does fail.
It fails reflexive because $a $~$a $ never happens. No-one is their own brother.
It fails symmetry for exactly the reason you state. If Allen, a boy, and Betty, girl, have the same parents than Allen is a full brother to Betty, but Betty is not a full brother to Allen.
Update!
Transitivity fails. If Allen is a full brother to Bob. And Bob is a full brother to Allen then Allen is not a full brother to Allen.
Transitivity fails.
===
I suppose we can define $a $~$b $ as 1) $a $ and be have the same parents, 2) $a $ is male, 3) $a $ and $b $ are different people.
Since no-one can 3) be a different person than oneself reflexivity can never happen. 2)Also being male may or may not occur. But 1) have same parents as self must always occur.
If $a $~$b $ then 1) $b$ and $a $ have same parents and 3) $b $
answered 19 mins ago
fleabloodfleablood
71.4k22686
$endgroup$
$begingroup$
I have corrected it. Does it read correct now?
$endgroup$
– Michael Ramage
17 mins ago
$begingroup$
Yes. it's a relation. But it's not an equivalence relation. It's not an equivalence relation because it fails. BTW I don't know why your book says transitivity fails.
$endgroup$
– fleablood
15 mins ago
$begingroup$
I understand. It is a book by my professor Alex McCallister, "A Transition to Advanced Mathematics: A Survey Course." I have spent several hours attempting to understand why transitivity fails, when it does not, unfortunately.
$endgroup$
– Michael Ramage
12 mins ago
$begingroup$
Got it! If $a$ and $b $ are both boys then $a=b$ and $b=a$ but $ane a$.
$endgroup$
– fleablood
4 mins ago
add a comment |
$begingroup$
Your title is inaccurate. An equivalence relationship can't fail symmetric and transitive properties, by definition, and this is not an equivalence relation because it does fail.
It fails reflexive because $a $~$a $ never happens. No-one is their own brother.
It fails symmetry for exactly the reason you state. If Allen, a boy, and Betty, girl, have the same parents than Allen is a full brother to Betty, but Betty is not a full brother to Allen.
Update!
Transitivity fails. If Allen is a full brother to Bob. And Bob is a full brother to Allen then Allen is not a full brother to Allen.
Transitivity fails.
===
I suppose we can define $a $~$b $ as 1) $a $ and be have the same parents, 2) $a $ is male, 3) $a $ and $b $ are different people.
Since no-one can 3) be a different person than oneself reflexivity can never happen. 2)Also being male may or may not occur. But 1) have same parents as self must always occur.
If $a $~$b $ then 1) $b$ and $a $ have same parents and 3) $b $
answered 19 mins ago
fleabloodfleablood
71.4k22686
$endgroup$
Your title is inaccurate. An equivalence relationship can't fail symmetric and transitive properties, by definition, and this is not an equivalence relation because it does fail.
It fails reflexive because $a $~$a $ never happens. No-one is their own brother.
It fails symmetry for exactly the reason you state. If Allen, a boy, and Betty, girl, have the same parents than Allen is a full brother to Betty, but Betty is not a full brother to Allen.
Update!
Transitivity fails. If Allen is a full brother to Bob. And Bob is a full brother to Allen then Allen is not a full brother to Allen.
Transitivity fails.
===
I suppose we can define $a $~$b $ as 1) $a $ and be have the same parents, 2) $a $ is male, 3) $a $ and $b $ are different people.
Since no-one can 3) be a different person than oneself reflexivity can never happen. 2)Also being male may or may not occur. But 1) have same parents as self must always occur.
If $a $~$b $ then 1) $b$ and $a $ have same parents and 3) $b $
answered 19 mins ago
fleabloodfleablood
71.4k22686
edited 6 mins ago
answered 19 mins ago
fleabloodfleablood
71.4k22686
answered 19 mins ago
fleabloodfleablood
71.4k22686
answered 19 mins ago
fleabloodfleablood
71.4k22686
71.4k22686
$begingroup$
I have corrected it. Does it read correct now?
$endgroup$
– Michael Ramage
17 mins ago
$begingroup$
Yes. it's a relation. But it's not an equivalence relation. It's not an equivalence relation because it fails. BTW I don't know why your book says transitivity fails.
$endgroup$
– fleablood
15 mins ago
$begingroup$
I understand. It is a book by my professor Alex McCallister, "A Transition to Advanced Mathematics: A Survey Course." I have spent several hours attempting to understand why transitivity fails, when it does not, unfortunately.
$endgroup$
– Michael Ramage
12 mins ago
$begingroup$
Got it! If $a$ and $b $ are both boys then $a=b$ and $b=a$ but $ane a$.
$endgroup$
– fleablood
4 mins ago
add a comment |
$begingroup$
I have corrected it. Does it read correct now?
$endgroup$
– Michael Ramage
17 mins ago
$begingroup$
Yes. it's a relation. But it's not an equivalence relation. It's not an equivalence relation because it fails. BTW I don't know why your book says transitivity fails.
$endgroup$
– fleablood
15 mins ago
$begingroup$
I understand. It is a book by my professor Alex McCallister, "A Transition to Advanced Mathematics: A Survey Course." I have spent several hours attempting to understand why transitivity fails, when it does not, unfortunately.
$endgroup$
– Michael Ramage
12 mins ago
$begingroup$
Got it! If $a$ and $b $ are both boys then $a=b$ and $b=a$ but $ane a$.
$endgroup$
– fleablood
4 mins ago
$begingroup$
I have corrected it. Does it read correct now?
$endgroup$
– Michael Ramage
17 mins ago
$begingroup$
I have corrected it. Does it read correct now?
$endgroup$
– Michael Ramage
17 mins ago
$begingroup$
Yes. it's a relation. But it's not an equivalence relation. It's not an equivalence relation because it fails. BTW I don't know why your book says transitivity fails.
$endgroup$
– fleablood
15 mins ago
$begingroup$
Yes. it's a relation. But it's not an equivalence relation. It's not an equivalence relation because it fails. BTW I don't know why your book says transitivity fails.
$endgroup$
– fleablood
15 mins ago
$begingroup$
I understand. It is a book by my professor Alex McCallister, "A Transition to Advanced Mathematics: A Survey Course." I have spent several hours attempting to understand why transitivity fails, when it does not, unfortunately.
$endgroup$
– Michael Ramage
12 mins ago
$begingroup$
I understand. It is a book by my professor Alex McCallister, "A Transition to Advanced Mathematics: A Survey Course." I have spent several hours attempting to understand why transitivity fails, when it does not, unfortunately.
$endgroup$
– Michael Ramage
12 mins ago
$begingroup$
Got it! If $a$ and $b $ are both boys then $a=b$ and $b=a$ but $ane a$.
$endgroup$
– fleablood
4 mins ago
$begingroup$
Got it! If $a$ and $b $ are both boys then $a=b$ and $b=a$ but $ane a$.
$endgroup$
– fleablood
4 mins ago
add a comment |
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