Question

If n(U)= 300, n(A)= 100, n(B)= 90 and n(A∩B)= 40 then find

(i) n0(A)
(ii) n0(B)
iii) n(A∪B)
iv) n(A ∪ B)'

Answer 1

To solve the set theory problem, complements and unions of sets were calculated using the principle of inclusion-exclusion and the properties of set complements within a universal set.

Step-by-step explanation:

The subject of the question is set theory in mathematics. The student is asked to find various elements related to two sets A and B within a universal set U.

1. n(A') refers to the number of elements in the complement of set A, which is the elements in the universal set U that are not in A. To find this, we subtract the number of elements in A from the total elements in U, i.e., n(A') = n(U) - n(A) = 300 - 100 = 200.
2. n(B') refers to the number of elements in the complement of set B. This is found similarly to n(A'), i.e., n(B') = n(U) - n(B) = 300 - 90 = 210.
3. To find n(A ∪ B), which is the number of elements in either set A or set B or both, we use the principle of inclusion-exclusion: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 100 + 90 - 40 = 150.
4. n((A ∪ B)') refers to the number of elements not in either A or B. Since we've found n(A ∪ B), we can find its complement by subtracting from the universal set: n((A ∪ B)') = n(U) - n(A ∪ B) = 300 - 150 = 150.