# More set theory trouble

• Nov 26th 2011, 01:31 PM
ehpoc
More set theory trouble
Ok so say the cardinality of.....

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

How do I find |ABC|

note:all adjacent sets are intersect. This completely vexes me.
• Nov 26th 2011, 01:51 PM
Plato
Re: More set theory trouble
Quote:

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

[TEX]A\cap B~\&~A\cup B[/TEX] gives $A\cap B~\&~A\cup B$.

From that given all you can say is $|ABC|\le \min\{|AB|,|AC|,|BC|\}=11$
• Nov 26th 2011, 02:18 PM
ehpoc
Re: More set theory trouble
I honestly do not understand how we can come to any single conclusion about |ABC|
• Nov 26th 2011, 02:23 PM
Plato
Re: More set theory trouble
Quote:

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: $\{0,1,\cdots,11\}$
• Nov 26th 2011, 02:29 PM
Also sprach Zarathustra
Re: More set theory trouble
Quote:

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

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

How do I find |ABC|

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

Inclusion
• Nov 26th 2011, 02:30 PM
ehpoc
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
• Nov 26th 2011, 02:50 PM
Plato
Re: More set theory trouble
Quote:

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.
$109=58+40+46-13-11-17+|ABC|$
• Nov 26th 2011, 10:48 PM
Annatala
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.)