If A and B be two sets containing 6 and 3 elements respectively, what can be the minimum number of elements in `AuuB` ? Also, find the maximum number of elements in `AuuB`.

Explanation

We have, `n(AuuB)=n(A)+n(B)-n(AnnB),n(AuuB)` is minimum or maximum according as `n(AnnB)` is maximum or minimum, respectively.
Case I If `n(AnnB)` is minimum i.e., `n(AnnB)` = 0 such that
A = {a, b, c, d, e, f} and B = {g, h, i}
`therefore n(AuuB)=n(A)+n(B)=6+3=9`
Case II If `n(AnnB)` is maximum i.e., `n(AnnB) = 3`, such that
A = {a, b, c, d, e, f} and B = {d, a, c}
`therefore n(AuuB)=n(A)+n(B)-n(AnnB)=6+3-3=6`