Cn

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- Feb 27th 2007, 08:57 AMchillerbros17Set Theory
Cn

- Feb 27th 2007, 09:22 AMThePerfectHacker
The minimum value is when

**all**the elements repeat.

That is, B is contained fully in A.

Thus, A U B = A.

Thus, |A U B|=|A|=r.

Quote:

(b) What is the maximum value of |A U B|?

Then |A U B| = |A|+|B| - |A (intersect) B| =|A|+|B| *

*)By inclusion-exclusion.

Quote:

(c) What is the minimum value of |A intersect B|?

That is A intersect B = empty.

Thus, |A intersect B| = 0.

Quote:

(d) What is the maximum value of |A intersect B|?

Then, A intersect B = B

Thus,

|A intersect B|=s.