Inclusion-Exclusion Quick Question

[Caldus]

If I am given data for four sets and am asked to find how many elements are in exactly two of these four sets, how would I approach the problem?

 

[matt grime]

inc exc in this case states, if i let the sets be 1,2,3,4 that

|1u2u3u4| = |1|+|2|+|3|+|4| - |1n2|-|1n3|-|1n4|-|2n3|-|2n4|-|3n4|+|1n2n3| +|1n2n4|+|2n3n4|-|1n2n3n4|

how you use that depends on the details of the question. that is assuming that is what you meant by "4 sets", which 4 sets? which two of them do you need to find the cardinality of the interesection of?

 

[Caldus]

If Universe = 75 and there for sets A1 - A4,

Each A has 28
Each intersection of two has 12 (Example: A1 n A2 = 12)
Each intersection of three has 5
Intersection of all sets equal 1

How do I go about finding how many elements are in exactly two sets?

 

[matt grime]

Let Bi be the complement of Ai, then you want to find the cardinalities of all sets like

A1nA2mB3nB4

oughtn't to be too hard after you've played around with all the set identities you can think of, but to be honest, that I've not done.