Q3 of 71 Page 30

If A and B are two sets containing 13 and 16 elements respectively, then find the minimum and maximum number of elements in A ∪ B?

Let A and B be two sets with n(A) = 13, n(B) = 16.


We have, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)



Minimum number of elements in A ∪ B is possible if all the elements of A lie in B, i.e. A⊆ B (B cannot be a subset of A, obviously, as n(B) > n(A)).


In that case, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)


n(A ∪ B) = 13 + 16 – 13 = 16



Maximum number of elements in A ∪ B is possible if n(A ∩ B) = 0,


i.e. if A and B are disjoint sets.


In that case, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)


n(A ∪ B) = 13 + 16 – 0 = 29


So, minimum and maximum number of elements possible in A ∪ B are 16 and 29 respectively.


More from this chapter

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1

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