How do I simplify â ð«ð«ð«Ã¢ÂÂ, ð«ð«Ã¢ÂÂ, ð«Ã¢ÂÂ, âÂÂ
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I'm not quite sure how to approach this problem. I know how to get the intersection of two sets but I don't know what to do with this kind of notation.
elementary-set-theory
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up vote
1
down vote
favorite
I'm not quite sure how to approach this problem. I know how to get the intersection of two sets but I don't know what to do with this kind of notation.
elementary-set-theory
2
It must be the intersection of the four sets enclosed into braces.
â Mauro ALLEGRANZA
Sep 7 at 7:23
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up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm not quite sure how to approach this problem. I know how to get the intersection of two sets but I don't know what to do with this kind of notation.
elementary-set-theory
I'm not quite sure how to approach this problem. I know how to get the intersection of two sets but I don't know what to do with this kind of notation.
elementary-set-theory
elementary-set-theory
edited Sep 7 at 7:23
Mauro ALLEGRANZA
61.5k446105
61.5k446105
asked Sep 7 at 7:20
Peter Celinski
423
423
2
It must be the intersection of the four sets enclosed into braces.
â Mauro ALLEGRANZA
Sep 7 at 7:23
add a comment |Â
2
It must be the intersection of the four sets enclosed into braces.
â Mauro ALLEGRANZA
Sep 7 at 7:23
2
2
It must be the intersection of the four sets enclosed into braces.
â Mauro ALLEGRANZA
Sep 7 at 7:23
It must be the intersection of the four sets enclosed into braces.
â Mauro ALLEGRANZA
Sep 7 at 7:23
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
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accepted
$cap$ can be recognized as the notation of an operator on non-empty sets characterized by:$$xincap aiffforall bin a;xin b$$
In that context the common expression $Acap B$ can be looked at as an abbreviation of $capA,B$ and $bigcap_iin IA_i$ as an abbreviation of $capA_imid iin I$.
So the set in the title of your question is the same as:$$varnothingcapwpvarnothingcapwpwpvarnothingcapwpwpwpvarnothing$$
where $wp(A):=Bmid Bsubseteq A$.
Can you take it from here?
Yes! Thanks a bunch, that's all I needed to understand this
â Peter Celinski
Sep 7 at 7:55
You are very welcome.
â drhab
Sep 7 at 7:56
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
$cap$ can be recognized as the notation of an operator on non-empty sets characterized by:$$xincap aiffforall bin a;xin b$$
In that context the common expression $Acap B$ can be looked at as an abbreviation of $capA,B$ and $bigcap_iin IA_i$ as an abbreviation of $capA_imid iin I$.
So the set in the title of your question is the same as:$$varnothingcapwpvarnothingcapwpwpvarnothingcapwpwpwpvarnothing$$
where $wp(A):=Bmid Bsubseteq A$.
Can you take it from here?
Yes! Thanks a bunch, that's all I needed to understand this
â Peter Celinski
Sep 7 at 7:55
You are very welcome.
â drhab
Sep 7 at 7:56
add a comment |Â
up vote
2
down vote
accepted
$cap$ can be recognized as the notation of an operator on non-empty sets characterized by:$$xincap aiffforall bin a;xin b$$
In that context the common expression $Acap B$ can be looked at as an abbreviation of $capA,B$ and $bigcap_iin IA_i$ as an abbreviation of $capA_imid iin I$.
So the set in the title of your question is the same as:$$varnothingcapwpvarnothingcapwpwpvarnothingcapwpwpwpvarnothing$$
where $wp(A):=Bmid Bsubseteq A$.
Can you take it from here?
Yes! Thanks a bunch, that's all I needed to understand this
â Peter Celinski
Sep 7 at 7:55
You are very welcome.
â drhab
Sep 7 at 7:56
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
$cap$ can be recognized as the notation of an operator on non-empty sets characterized by:$$xincap aiffforall bin a;xin b$$
In that context the common expression $Acap B$ can be looked at as an abbreviation of $capA,B$ and $bigcap_iin IA_i$ as an abbreviation of $capA_imid iin I$.
So the set in the title of your question is the same as:$$varnothingcapwpvarnothingcapwpwpvarnothingcapwpwpwpvarnothing$$
where $wp(A):=Bmid Bsubseteq A$.
Can you take it from here?
$cap$ can be recognized as the notation of an operator on non-empty sets characterized by:$$xincap aiffforall bin a;xin b$$
In that context the common expression $Acap B$ can be looked at as an abbreviation of $capA,B$ and $bigcap_iin IA_i$ as an abbreviation of $capA_imid iin I$.
So the set in the title of your question is the same as:$$varnothingcapwpvarnothingcapwpwpvarnothingcapwpwpwpvarnothing$$
where $wp(A):=Bmid Bsubseteq A$.
Can you take it from here?
edited Sep 7 at 11:52
answered Sep 7 at 7:40
drhab
89.2k541123
89.2k541123
Yes! Thanks a bunch, that's all I needed to understand this
â Peter Celinski
Sep 7 at 7:55
You are very welcome.
â drhab
Sep 7 at 7:56
add a comment |Â
Yes! Thanks a bunch, that's all I needed to understand this
â Peter Celinski
Sep 7 at 7:55
You are very welcome.
â drhab
Sep 7 at 7:56
Yes! Thanks a bunch, that's all I needed to understand this
â Peter Celinski
Sep 7 at 7:55
Yes! Thanks a bunch, that's all I needed to understand this
â Peter Celinski
Sep 7 at 7:55
You are very welcome.
â drhab
Sep 7 at 7:56
You are very welcome.
â drhab
Sep 7 at 7:56
add a comment |Â
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2
It must be the intersection of the four sets enclosed into braces.
â Mauro ALLEGRANZA
Sep 7 at 7:23