Question

The sets A and B are having elements 10 and 8,n(A ∩ B) =2, the n(A ∪B) is_____

A. 10
B. 12
C. 14
D. 16

Answer 1

The number of elements in the union of sets A and B, denoted as n(A ∪ B), can be calculated using the formula n(A) + n(B) - n(A ∩ B), which equals 16 for the given sets.

Step-by-step explanation:

The student is asking about the principles of set theory, specifically about calculating the number of elements in the union of two sets when given the number of elements in each set and their intersection.

To calculate the number of elements in the union n(A ∪ B), we use the formula n(A) + n(B) - n(A ∩ B). The values given are n(A) = 10, n(B) = 8, and n(A ∩ B) = 2.

Substituting these values into the formula gives us the solution:

n(A ∪ B) = 10 + 8 - 2 = 16. So the correct answer is D. 16.