how to calculate these intersections without having to write

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ISAwill
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how to calculate these intersections without having to write

Postby ISAwill » Thu Oct 30, 2014 10:20 pm UTC

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

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Qaanol
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Re: how to calculate these intersections without having to w

Postby Qaanol » Fri Oct 31, 2014 10:04 pm UTC

Is this homework?

Can you see which of the sets are equal to each other?
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jestingrabbit
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Re: how to calculate these intersections without having to w

Postby jestingrabbit » Sat Nov 01, 2014 1:09 am UTC

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
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Re: how to calculate these intersections without having to w

Postby DavCrav » Thu Nov 06, 2014 11:36 pm UTC

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


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