how to calculate these intersections without having to write

For the discussion of math. Duh.

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ISAwill
Posts: 1
Joined: Thu Oct 30, 2014 10:15 pm UTC

how to calculate these intersections without having to write

We have the following sets:

X=(a,b,c,d)∈S:b<c<d,
Y=(a,b,c,d)∈S:a<c<d,
Z=(a,b,c,d)∈S:a<b<d,
F=(a,b,c,d)∈S:a<b<c,
Where each of a,b,c,d have integer values from 1 to 5

How to calculate |X∩Y|, |X∩Z|, |Z∩F|, |X∩Y∩Z|, |X∩Y∩Z∩F| without the need to write down all possible combinations

Qaanol
The Cheshirest Catamount
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Joined: Sat May 09, 2009 11:55 pm UTC

Re: how to calculate these intersections without having to w

Is this homework?

Can you see which of the sets are equal to each other?
wee free kings

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

Re: how to calculate these intersections without having to w

if x is in A∩B, the x is in A and x is in B. If A is all the things that satisfy conditionA, and B is all the things that satisfy conditionB, then x satisfies both conditionA and conditionB. That's all you really need.
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DavCrav
Posts: 251
Joined: Tue Aug 12, 2008 3:04 pm UTC
Location: Oxford, UK

Re: how to calculate these intersections without having to w

The first and third of these sets have equal size, and there's a nice bijection between them, if you can spot it.