The minimum value is whenallthe elements repeat.

That is, B is contained fully in A.

Thus, A U B = A.

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

When all elements are distincy, that is A and B are disjoint.(b) What is the maximum value of |A U B|?

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

*)By inclusion-exclusion.

When A and B are disjoint.(c) What is the minimum value of |A intersect B|?

That is A intersect B = empty.

Thus, |A intersect B| = 0.

When B is fully contained in A.(d) What is the maximum value of |A intersect B|?

Then, A intersect B = B

Thus,

|A intersect B|=s.