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Sets A and B have 3 and 6 elements respe...

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A `uu` B ?

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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`
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