Discrete Math

[Nadja]

Can someone please help me with this question?

 

Given sets A, B, C and D.

Each volume contains exactly six elements.

Each section of the two of them (A ∩ B, A ∩ C, A ∩ D, B ∩ C, B ∩ D or C ∩ D)

contains exactly two elements.

a) Give a concrete example showing that this is possible.

b ) How many elements contain the amount of (A - B ) × (C - D)

Edited November 18, 2010 by Nadja

[the tree]

Part ( a ) can easily be done simply by drawing a venn diagram, remembering to give each element a unique index (you know, just number then 1,2,3,4,5...).

 

Once you've done that, for part ( b ) you can use your venn diagram to count the amount of elements in A-B and C-D. I'll tell you for free that |AxB|=|A|x|B|.

Edited November 18, 2010 by the tree

[Nadja]

Thnx, But it's really difficult to draw a Venn diagram showing that all elements are interdependent. Or I guess it does, but it wont be a good looking one.

Edited November 20, 2010 by Nadja

[the tree]

Thnx, But it's really difficult to draw a Venn diagram showing that all elements are interdependent.

No it isn't. This took me much less than a minute. As a further tip, in the first construction that came to mind for me, there were no elements that appeared in more than two of A,B,C or D.

Or I guess it does, but it wont be a good looking one

Well no, but I'm assuming your not a fine arts major, so I wouldn't worry about that. Edited November 21, 2010 by the tree