Answer :

Number of elements in set A n(A) = 3 and number of elements in set B n(B) = 5

The number of elements in A ∪ B is n(A ∪ B).

i) Now for elements in A ∪ B to be maximum, there should not be any intersection between both sets that is A and B both sets must be disjoint sets as shown.

Hence the number of elements in A ∪ B is n(A ∪ B) = n(A) + n(B)

⇒ n(A ∪ B) = 3 + 5

⇒ n(A ∪ B) = 8

Hence maximum number of elements in A ∪ B is 8

ii) Now for a number of elements in A ∪ B to be minimum, there should be an intersection between sets A and B so that some elements are common

The count will be minimum when all the elements from set A are also in set B the reverse are not possible because n(A) < n(B)

Hence if the 3 elements of A are in the intersection of A and B, then the number of elements only in B will be 2 because n(B) = 5

Visually it is represented as,

As seen from the figure the number of elements in A ∪ B is 5 hence minimum number of elements in A ∪ B = 5

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