Question

Suppose n(A) = 100, n(B) = 200, n(C) = 300, n(A ∩ B) = 10, n(A ∩ C) = 15, n(B ∩ C) = 20, n(A ∩ B ∩ C) = 5, n(A ∪ B ∪ C) = ___.

a. 570
b. 595
c. 610
d. 630

Answer 1

To find the number of elements in the union of sets A, B, and C, we can use the principle of inclusion-exclusion.

Step-by-step explanation:

The problem provides information about the number of elements in sets A, B, and C, as well as the number of elements in their intersections. To find the number of elements in the union of A, B, and C (n(A ∪ B ∪ C)), we can use the principle of inclusion-exclusion.

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)

Plugging in the given values, we can calculate:

n(A ∪ B ∪ C) = 100 + 200 + 300 - 10 - 15 - 20 + 5 = 560

Therefore, the correct answer is a. 570.