Question

Let A,B, and C be given sets with n(A)=3, n(B)=5. Find the maximum value of n(A∪B).

A) 5
B) 6
C) 7
D) 8

Answer 1

The maximum value of n(A∪B), the number of elements in the union of sets A and B, equals the sum of elements in each set if there is no overlap, which is 3 + 5 = 8.

Step-by-step explanation:

The question asks us to find the maximum value of n(A∪B), which is the number of elements in the union of sets A and B. Given that n(A) is the number of elements in set A and n(B) is the number of elements in set B, and these are 3 and 5 respectively, the maximum number of elements in the union set A∪B occurs when there is no overlap between sets A and B.

Therefore, the maximum value of n(A∪B) is the sum of the number of elements in set A and set B, which is n(A) + n(B) = 3 + 5 = 8. This would happen if none of the elements in set A are in set B, meaning there is no intersection between sets A and B.

So, the correct answer is D) 8.