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- Oct 28th 2006, 01:21 AM #1

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## need help!!!

If we have two sets, A and B, contained in the universal set

Can someone tell me why the smallest possible number of elements of

(A intersect B) occurs when A union B = universal set???

i know that

n(A intersect B) = n(A) + n(B) - n(A union B)

so to make it smaller, we need to make n(A union B) as big as possible.

But is there a way to explain this without using the formula above???

- Oct 28th 2006, 03:17 AM #2

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- Oct 28th 2006, 03:25 AM #3

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- Oct 28th 2006, 03:40 AM #4

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Because n(A)+n(B)>n(U), there must be some elements shared between

A and B. The smallest number that could be shared is 6 (that is:

n(A)+n(B)-n(U), any smaller number of shared elements will leave n(A Union

B)>60, which would be a contradiction).

But if A and B share exactly 6 elements then n(A Union B)=60, and so

A Union B=U.

RonL

RonL