Let A, B, and C be sets in a universal set U. We are given n(U) = 58, n(A) = 23, n(B) = 21, n(C) = 23, n(A ∩ B) = 8, n(A ∩ C) = 6, n(B ∩ C) = 11, n(A ∩ B ∩ CC) = 4. Find the following values.

1. Find n(AUB) for each pair of sets described. a) n(A)-10, n(B)-8, n(AB)-4 b) n(A)-7, n(B)-12. ACB

Let A, B, C subset U. Suppose that n(U)= 41, n(A)= 30 and n(B)= 35. For each of the following sets, give the smallest possible number of elements the set can contain and the largest number of elements the set can contain. If you know the exact number of elements the set has, then write the same number in both spaces. 1. A U B What is the smallest and largest possible values. 2. A intersect B What is the smallest and largest possible values. 3. A’ What is the smallest and largest possible values. 4. A’ intersect B What is the smallest and largest possible values. 5. A’ U B What is the smallest and largest possible values.

Let A and B be finite sets. (a) Explain why n(ANB) s n(A). (b) Explain why n(A) s n(AUB). (c) Suppose n(ANB) = n(AUB). What more can be said about A and B? (a) Explain why n(ANB) s n(A). Choose the correct answer below.