I. True/False
1. A = B if and only if B ∈ A and A ∈ B.
2. A ∩ (B ? C) = (A ? B) ∩ (A ? C)
3. (Ac) c = A
4. B ∩ Bc = Ø
5. If A and B are two sets that are not disjoint, then n(A ? B) = n(A) + n(B).
6. If x ∈ (A ∪ B), then x ∈ A and x ∈ B.
7. If x ∈ A and A ⊂ B, then x ∉ B.
8. If B = {1}, then the subsets of B include {1) and {Ø}.
II. Multiple Choice
10. If x ⊂ (C ∪ D) then it is possible that
a. x ∈ C but x ∉ D
b. x ∈ Cc
c. x ⊂ Cc
d. x ∉ D and x ∉ C
III. Matching
11. e
For disjoint sets, n(A ∪ B) = n(A) + n(B)
12. a
For not disjoint sets, n (A ∪ B) = n(A) + n(B) - n(A ∩ B)
IV. Fill in the Blank
13. __________________ notation is the standard notation to use when denoting sets (such as A = {1, 2, 3}), but ___________________________ notation is just as effective, although it does not require more writing.
14. When two sets have nothing in common they are said to be __________________, which is denoted by n(A ∩ B) = __________________________________.
15. If there are 3 ways of performing task T and 2 ways of performing task Q, then I can determine that there are ____ number of ways of performing task T followed by task Q using the ______Principle.
V. Short Answer
16 b. Consider the new universal set U with subsets C and D, where n(U) = 250, n(C) = 120, n (C ∪ D) = 130, and n(C ∩ D) = 60. Answer the following:
i. What is n(Cc)?
ii. What is n(D)?
iii. What is n(Dc)?
iv. Draw all of this using Venn Diagrams. Be sure to indicate n(U), n(C), n(D), and n(C ∩ D) in your illustration.
Using three circle Venn Diagrams (with the universal set U and subsets A, B, and C), shade the portion that corresponds to the following:
17 b. (A ∩ Bc) ∪ C
18. Let U= {5,10,15,20} and let A = {5,15,20}, B = {5,10,15}, and C = {5, 20}. Answer the following questions:
a. What are all of the subsets of U? List them all.
b. List the elements of the set (C ∪ Bc).
c. List the elements of (A ∩ C)c.
d. List the elements of Ac ∪ (B ∩ C)c.
e. Regarding the subsets A, B, and C, which is a subset of the other? Please show using proper notation.