Mixing
What is meant by “relation between sets” in this question?
$begingroup$
A homework question asks,
Consider any two sets $A$ and $B$. What should the relation between $A$ and $B$ be, so that $(𝐴 ∩ 𝐵) × 𝐵 = 𝐵 × (𝐴 ∩ 𝐵)$. Prove your answer
I am not looking for an answer to the problem, but I’m not understanding what it is asking for. I think it’s asking “is $A$ a subset of $B$, vice versa, etc” but I’m not sure.
discrete-mathematics
edited Jan 17 at 21:27
egreg
183k1486204
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
$endgroup$
add a comment |
$begingroup$
A homework question asks,
Consider any two sets $A$ and $B$. What should the relation between $A$ and $B$ be, so that $(𝐴 ∩ 𝐵) × 𝐵 = 𝐵 × (𝐴 ∩ 𝐵)$. Prove your answer
I am not looking for an answer to the problem, but I’m not understanding what it is asking for. I think it’s asking “is $A$ a subset of $B$, vice versa, etc” but I’m not sure.
discrete-mathematics
edited Jan 17 at 21:27
egreg
183k1486204
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
$endgroup$
$begingroup$
it could be $A=B$
$endgroup$
– janmarqz
Jan 17 at 20:10
add a comment |
$begingroup$
A homework question asks,
Consider any two sets $A$ and $B$. What should the relation between $A$ and $B$ be, so that $(𝐴 ∩ 𝐵) × 𝐵 = 𝐵 × (𝐴 ∩ 𝐵)$. Prove your answer
I am not looking for an answer to the problem, but I’m not understanding what it is asking for. I think it’s asking “is $A$ a subset of $B$, vice versa, etc” but I’m not sure.
discrete-mathematics
edited Jan 17 at 21:27
egreg
183k1486204
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
$endgroup$
A homework question asks,
Consider any two sets $A$ and $B$. What should the relation between $A$ and $B$ be, so that $(𝐴 ∩ 𝐵) × 𝐵 = 𝐵 × (𝐴 ∩ 𝐵)$. Prove your answer
I am not looking for an answer to the problem, but I’m not understanding what it is asking for. I think it’s asking “is $A$ a subset of $B$, vice versa, etc” but I’m not sure.
discrete-mathematics
discrete-mathematics
edited Jan 17 at 21:27
egreg
183k1486204
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
edited Jan 17 at 21:27
egreg
183k1486204
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
edited Jan 17 at 21:27
egreg
183k1486204
edited Jan 17 at 21:27
egreg
183k1486204
edited Jan 17 at 21:27
egreg
183k1486204
183k1486204
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
asked Jan 17 at 20:08
Dallin HagmanDallin Hagman
1
1
$begingroup$
it could be $A=B$
$endgroup$
– janmarqz
Jan 17 at 20:10
add a comment |
$begingroup$
it could be $A=B$
$endgroup$
– janmarqz
Jan 17 at 20:10
$begingroup$
it could be $A=B$
$endgroup$
– janmarqz
Jan 17 at 20:10
$begingroup$
it could be $A=B$
$endgroup$
– janmarqz
Jan 17 at 20:10
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The question indeed asks you to find some inclusion relation between $A$ and $B$ such that the relation holds. Or some other condition that you should find.
You can start by observing that if $B=emptyset$ or $Acap B=emptyset$, then the statement holds. Thus you can go on with the assumption that neither set is empty.
What can you conclude from $Xtimes Y=Ytimes X$ if $X$ and $Y$ are not empty?
answered Jan 17 at 21:29
egregegreg
183k1486204
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The question indeed asks you to find some inclusion relation between $A$ and $B$ such that the relation holds. Or some other condition that you should find.
You can start by observing that if $B=emptyset$ or $Acap B=emptyset$, then the statement holds. Thus you can go on with the assumption that neither set is empty.
What can you conclude from $Xtimes Y=Ytimes X$ if $X$ and $Y$ are not empty?
answered Jan 17 at 21:29
egregegreg
183k1486204
$endgroup$
add a comment |
$begingroup$
The question indeed asks you to find some inclusion relation between $A$ and $B$ such that the relation holds. Or some other condition that you should find.
You can start by observing that if $B=emptyset$ or $Acap B=emptyset$, then the statement holds. Thus you can go on with the assumption that neither set is empty.
What can you conclude from $Xtimes Y=Ytimes X$ if $X$ and $Y$ are not empty?
answered Jan 17 at 21:29
egregegreg
183k1486204
$endgroup$
add a comment |
$begingroup$
The question indeed asks you to find some inclusion relation between $A$ and $B$ such that the relation holds. Or some other condition that you should find.
You can start by observing that if $B=emptyset$ or $Acap B=emptyset$, then the statement holds. Thus you can go on with the assumption that neither set is empty.
What can you conclude from $Xtimes Y=Ytimes X$ if $X$ and $Y$ are not empty?
answered Jan 17 at 21:29
egregegreg
183k1486204
$endgroup$
The question indeed asks you to find some inclusion relation between $A$ and $B$ such that the relation holds. Or some other condition that you should find.
You can start by observing that if $B=emptyset$ or $Acap B=emptyset$, then the statement holds. Thus you can go on with the assumption that neither set is empty.
What can you conclude from $Xtimes Y=Ytimes X$ if $X$ and $Y$ are not empty?
answered Jan 17 at 21:29
egregegreg
183k1486204
answered Jan 17 at 21:29
egregegreg
183k1486204
answered Jan 17 at 21:29
egregegreg
183k1486204
answered Jan 17 at 21:29
egregegreg
183k1486204
183k1486204
add a comment |
add a comment |
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$begingroup$
it could be $A=B$
$endgroup$
– janmarqz
Jan 17 at 20:10