Question

Given three subsets, a, b, and c, belonging to a universe U with the following properties: n(a) = 86, n(b) = 82, n(c) = 55, n(a ∩ b) = 18, n(a ∩ c) = 35, n(b ∩ c) = 43, and n(a ∩ b ∩ c) = 135.

Find n(a ∩ b ∩ c)

Answer 1

There is an error in the provided numbers because n(a ∩ b ∩ c) cannot exceed the sizes of the individual sets (n(a), n(b), n(c)). Therefore, an accurate answer cannot be determined with the given data.

Step-by-step explanation:

The student is asking to find the number of elements in the intersection of three subsets a, b, and c. There appears to be a mistake in the given problem as the number for n(a ∩ b ∩ c) exceeds the individual counts of the sets, which is not possible. Typically, to solve such problems, one would use the inclusion-exclusion principle.

However, with the provided numbers, an accurate calculation cannot be performed since n(a ∩ b ∩ c) cannot be greater than n(a), n(b), or n(c). The likely correct situation is that n(a ∩ b ∩ c) is less than or equal to all individual set counts. A typical formula used if the given numbers were correct would be: n(a ∩ b ∩ c) = n(a) + n(b) + n(c) - n(a ∩ b) - n(b ∩ c) - n(a ∩ c) + n(a ∩ b ∩ c), but this cannot be applied here.