# Thread: More set theory trouble

1. ## More set theory trouble

Ok so say the cardinality of.....

$\displaystyle U=120 ,A=58, B=40, C=46 AB=13,AC=11,BC=17$

How do I find |ABC|

note:all adjacent sets are intersect. This completely vexes me.

2. ## Re: More set theory trouble

Originally Posted by ehpoc
Ok so say the cardinality of.....
$\displaystyle U=120 ,A=58, B=40, C=46 AB=13,AC=11,BC=17$
How do I find |ABC|
note:all adjacent sets are intersect. This completely vexes me.
[TEX]A\cap B~\&~A\cup B[/TEX] gives $\displaystyle A\cap B~\&~A\cup B$.

From that given all you can say is $\displaystyle |ABC|\le \min\{|AB|,|AC|,|BC|\}=11$

3. ## Re: More set theory trouble

I honestly do not understand how we can come to any single conclusion about |ABC|

4. ## Re: More set theory trouble

Originally Posted by ehpoc
I honestly do not understand how we can come to any single conclusion about |ABC|
No one can. There are twelve different possible values: $\displaystyle \{0,1,\cdots,11\}$

5. ## Re: More set theory trouble

Originally Posted by ehpoc
Ok so say the cardinality of.....

$\displaystyle U=120 ,A=58, B=40, C=46 AB=13,AC=11,BC=17$

How do I find |ABC|

note:all adjacent sets are intersect. This completely vexes me.
Inclusion

6. ## Re: More set theory trouble

So when a question ask "What is |ABC|" it is not really asking that? Why would the question not ask what is the maximum that |ABC| could be?

So when you say 11 you are saying "there is at most 11 elements in ABC"?

Oh btw I just realized that I missed out one key premise.... AuBuC=109 I think I can solve it now. I keep getting psyched out by these problems and choking really.

EDIT: nope still can't solve it. LOL

7. ## Re: More set theory trouble

Originally Posted by ehpoc
So when a question ask "What is |ABC|" it is not really asking that? Why would the question not ask what is the maximum that |ABC| could be?
Oh btw I just realized that I missed out one key premise.... AuBuC=109 [/QUOTE]
Now it can be solved.
$\displaystyle 109=58+40+46-13-11-17+|ABC|$

8. ## Re: More set theory trouble

If you're having trouble visualizing this, a Venn Diagram is just what the doctor ordered. (Particularly with three sets, where all intersections are represented.)