How do I simplify ⋂ 𝒫𝒫𝒫⌀, 𝒫𝒫⌀, 𝒫⌀, ⌀

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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.










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    It must be the intersection of the four sets enclosed into braces.
    – Mauro ALLEGRANZA
    Sep 7 at 7:23














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.










share|cite|improve this question



















  • 2




    It must be the intersection of the four sets enclosed into braces.
    – Mauro ALLEGRANZA
    Sep 7 at 7:23












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.










share|cite|improve this question















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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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.
    – Mauro ALLEGRANZA
    Sep 7 at 7:23












  • 2




    It must be the intersection of the four sets enclosed into braces.
    – Mauro ALLEGRANZA
    Sep 7 at 7:23







2




2




It must be the intersection of the four sets enclosed into braces.
– Mauro ALLEGRANZA
Sep 7 at 7:23




It must be the intersection of the four sets enclosed into braces.
– Mauro ALLEGRANZA
Sep 7 at 7:23










1 Answer
1






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?






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  • Yes! Thanks a bunch, that's all I needed to understand this
    – Peter Celinski
    Sep 7 at 7:55










  • You are very welcome.
    – drhab
    Sep 7 at 7:56










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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?






share|cite|improve this answer






















  • Yes! Thanks a bunch, that's all I needed to understand this
    – Peter Celinski
    Sep 7 at 7:55










  • You are very welcome.
    – drhab
    Sep 7 at 7:56














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?






share|cite|improve this answer






















  • Yes! Thanks a bunch, that's all I needed to understand this
    – Peter Celinski
    Sep 7 at 7:55










  • You are very welcome.
    – drhab
    Sep 7 at 7:56












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?






share|cite|improve this answer














$cap$ 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?







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








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
    – Peter Celinski
    Sep 7 at 7:55










  • You are very welcome.
    – drhab
    Sep 7 at 7:56
















  • Yes! Thanks a bunch, that's all I needed to understand this
    – Peter Celinski
    Sep 7 at 7:55










  • You are very welcome.
    – drhab
    Sep 7 at 7:56















Yes! Thanks a bunch, that's all I needed to understand this
– Peter Celinski
Sep 7 at 7:55




Yes! Thanks a bunch, that's all I needed to understand this
– Peter Celinski
Sep 7 at 7:55












You are very welcome.
– drhab
Sep 7 at 7:56




You are very welcome.
– drhab
Sep 7 at 7:56

















 

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