Question

If n(A)= 12, n(B)=15, and n(AnB)=0, the what is n(AuB)?

a. 27
b. 3
c. 12
d. 15

Answer 1

To calculate the number of elements in the union of sets A and B, apply the inclusion-exclusion principle: n(A) + n(B) - n(A ∩ B). Given n(A) = 12, n(B) = 15, and n(A ∩ B) = 0, the number of elements in n(A ∪ B) is 27.

Step-by-step explanation:

The student is asking about the calculation of the number of elements in the union of two sets A and B when given the number of elements in each set and being told that the intersection is empty. Using the principle of inclusion-exclusion, the formula for finding the number of elements in the union A ∪ B is n(A) + n(B) - n(A ∩ B). Since it is given that n(A) = 12, n(B) = 15, and the sets have no elements in common n(A ∩ B) = 0, the calculation will be 12 + 15 - 0 = 27.