Property of set exclusion set.
Clash Royale CLAN TAG#URR8PPP
up vote
7
down vote
favorite
Let $T$ have the property that for all sets $A, B in T$ we have that $(Abackslash B) in T$.
How can I prove that $forall A,B in T, Acap B in T$?
I was thinking I should start with both expressions:
$(Abackslash B) in T$.
$(Bbackslash A) in T$.
and show that$ (A cup B)backslash((Abackslash B)cup (B backslash A)=Acap B in T$.
I'm not sure how to show that the final part is in that set. It doesn't say anything about unions.
elementary-set-theory
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
add a comment |Â
up vote
7
down vote
favorite
Let $T$ have the property that for all sets $A, B in T$ we have that $(Abackslash B) in T$.
How can I prove that $forall A,B in T, Acap B in T$?
I was thinking I should start with both expressions:
$(Abackslash B) in T$.
$(Bbackslash A) in T$.
and show that$ (A cup B)backslash((Abackslash B)cup (B backslash A)=Acap B in T$.
I'm not sure how to show that the final part is in that set. It doesn't say anything about unions.
elementary-set-theory
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
add a comment |Â
up vote
7
down vote
favorite
up vote
7
down vote
favorite
Let $T$ have the property that for all sets $A, B in T$ we have that $(Abackslash B) in T$.
How can I prove that $forall A,B in T, Acap B in T$?
I was thinking I should start with both expressions:
$(Abackslash B) in T$.
$(Bbackslash A) in T$.
and show that$ (A cup B)backslash((Abackslash B)cup (B backslash A)=Acap B in T$.
I'm not sure how to show that the final part is in that set. It doesn't say anything about unions.
elementary-set-theory
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
Let $T$ have the property that for all sets $A, B in T$ we have that $(Abackslash B) in T$.
How can I prove that $forall A,B in T, Acap B in T$?
I was thinking I should start with both expressions:
$(Abackslash B) in T$.
$(Bbackslash A) in T$.
and show that$ (A cup B)backslash((Abackslash B)cup (B backslash A)=Acap B in T$.
I'm not sure how to show that the final part is in that set. It doesn't say anything about unions.
elementary-set-theory
elementary-set-theory
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
edited Sep 5 at 18:53
Asaf Karagila♦
295k32411739
295k32411739
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
asked Sep 5 at 18:43
WesleyGroupshaveFeelingsToo
340113
340113
add a comment |Â
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
11
down vote
accepted
Hint: $Acap B=Asetminus (Asetminus B)$
answered Sep 5 at 18:47
b00n heT
8,95511833
1
Hold that thought.
– WesleyGroupshaveFeelingsToo
Sep 5 at 18:48
2
Beat me to it! +1
– Fimpellizieri
Sep 5 at 18:48
I just had to show that these two were equivalent and that did the trick, thanks guys.
– WesleyGroupshaveFeelingsToo
Sep 5 at 19:34
add a comment |Â
up vote
8
down vote
Write $Acap B = Asetminus(Asetminus B)$.
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
11
down vote
accepted
Hint: $Acap B=Asetminus (Asetminus B)$
answered Sep 5 at 18:47
b00n heT
8,95511833
1
Hold that thought.
– WesleyGroupshaveFeelingsToo
Sep 5 at 18:48
2
Beat me to it! +1
– Fimpellizieri
Sep 5 at 18:48
I just had to show that these two were equivalent and that did the trick, thanks guys.
– WesleyGroupshaveFeelingsToo
Sep 5 at 19:34
add a comment |Â
up vote
11
down vote
accepted
Hint: $Acap B=Asetminus (Asetminus B)$
answered Sep 5 at 18:47
b00n heT
8,95511833
1
Hold that thought.
– WesleyGroupshaveFeelingsToo
Sep 5 at 18:48
2
Beat me to it! +1
– Fimpellizieri
Sep 5 at 18:48
I just had to show that these two were equivalent and that did the trick, thanks guys.
– WesleyGroupshaveFeelingsToo
Sep 5 at 19:34
add a comment |Â
up vote
11
down vote
accepted
up vote
11
down vote
accepted
Hint: $Acap B=Asetminus (Asetminus B)$
answered Sep 5 at 18:47
b00n heT
8,95511833
Hint: $Acap B=Asetminus (Asetminus B)$
answered Sep 5 at 18:47
b00n heT
8,95511833
answered Sep 5 at 18:47
b00n heT
8,95511833
answered Sep 5 at 18:47
b00n heT
8,95511833
answered Sep 5 at 18:47
b00n heT
8,95511833
8,95511833
1
Hold that thought.
– WesleyGroupshaveFeelingsToo
Sep 5 at 18:48
2
Beat me to it! +1
– Fimpellizieri
Sep 5 at 18:48
I just had to show that these two were equivalent and that did the trick, thanks guys.
– WesleyGroupshaveFeelingsToo
Sep 5 at 19:34
add a comment |Â
1
Hold that thought.
– WesleyGroupshaveFeelingsToo
Sep 5 at 18:48
2
Beat me to it! +1
– Fimpellizieri
Sep 5 at 18:48
I just had to show that these two were equivalent and that did the trick, thanks guys.
– WesleyGroupshaveFeelingsToo
Sep 5 at 19:34
1
1
Hold that thought.
– WesleyGroupshaveFeelingsToo
Sep 5 at 18:48
Hold that thought.
– WesleyGroupshaveFeelingsToo
Sep 5 at 18:48
2
2
Beat me to it! +1
– Fimpellizieri
Sep 5 at 18:48
Beat me to it! +1
– Fimpellizieri
Sep 5 at 18:48
I just had to show that these two were equivalent and that did the trick, thanks guys.
– WesleyGroupshaveFeelingsToo
Sep 5 at 19:34
I just had to show that these two were equivalent and that did the trick, thanks guys.
– WesleyGroupshaveFeelingsToo
Sep 5 at 19:34
add a comment |Â
up vote
8
down vote
Write $Acap B = Asetminus(Asetminus B)$.
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
add a comment |Â
up vote
8
down vote
Write $Acap B = Asetminus(Asetminus B)$.
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
add a comment |Â
up vote
8
down vote
up vote
8
down vote
Write $Acap B = Asetminus(Asetminus B)$.
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
Write $Acap B = Asetminus(Asetminus B)$.
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
answered Sep 5 at 18:48
Fimpellizieri
16.9k11836
16.9k11836
add a comment |Â
add a comment |Â
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