What am I doing wrong on this simple cardinality of unions/intersections problem?

**AxiomOfChoice** · Jun22-09, 04:18 PM

If I know:

$LaTeX Code: |A \\cup B \\cup C|$ = 1000

= 344

= 572

**mathman** · Jun22-09, 05:55 PM

How did you get 554?

**AxiomOfChoice** · Jun22-09, 05:57 PM

Originally Posted by mathman

How did you get 554?

Using the following formula:

$LaTeX Code: |A \\cup B \\cup C| = |A| + |B| + |C| - |A \\cap B| - |B \\cap C| - |A \\cap C| + |A \\cap B \\cap C|$

**HallsofIvy** · Jun22-09, 06:14 PM

Originally Posted by AxiomOfChoice

Using the following formula:

$LaTeX Code: |A \\cup B \\cup C| = |A| + |B| + |C| - |A \\cap B| - |B \\cap C| - |A \\cap C| + |A \\cap B \\cap C|$

So 1000= 344+ 572+ 296- 301- 572- 296+ x.

Then you appear to have just done the arithmetic wrong. Solving this equation for x does not give anything like 554!

**AxiomOfChoice** · Jun22-09, 06:17 PM

Originally Posted by HallsofIvy

So 1000= 344+ 572+ 296- 301- 572- 296+ x.

Then you appear to have just done the arithmetic wrong. Solving this equation for x does not give anything like 554!

...are you quite sure what you wrote is correct?

**mathman** · Jun22-09, 11:02 PM

Final analysis: The data is wrong. |A|+|B|+|C|=1212. This allows only 212 for any overlap. Since each of the pairwise intersections is more, this is impossible.

Note: minor error in the 1000= statement, the -296 should be -213, but it doesn't change the analysis.