c
Math 141 WIR, Spring 2007, Benjamin
Aurispa
Math 141 Week-in-Review 5 Answer Key
1. (a) TRUE
(b) FALSE (A is a subset of C, but not a proper subset.)
(c) TRUE
(d) TRUE
(e) TRUE (The empty set is a subset of EVERY set.)
(f) TRUE
(g) FALSE (5 is an element of B, not a subset. You can make this correct by saying 5 ∈ B
or {5} ⊂ B.)
(h) FALSE ({1} is a subset of C, not an element. You could make this statement correct by
saying 1 ∈ C or {1} ⊂ C.)
2. (a) {6}
(b) {9}
(c) {3, 7}
(d) {1, 2, 4, 5, 7, 8, 10}
(e) ∅
3. See Full Solutions from live review for shaded diagrams.
4. (a) The set of students who listen to country but not pop.
(b) The set of students who do not listen to rock or do listen to pop.
(a) C ∪ R ∪ P
(b) C c ∩ Rc OR (C ∪ R)c (De Morgan’s Laws tell us these are equal.)
(c) (R ∪ P ) ∩ C c
5. (a) 93
(b) 23
(c) 41
(d) 70
6. (a) 21
(b) 179
(c) 25
(d) 115
7. (a) 92
(b) 39
(c) 30
1
c
Math 141 WIR, Spring 2007, Benjamin
Aurispa
(d) 65
8. 4 · 5 · 3 · 6 = 360 different sandwiches are possible.
9. 25 · 515 ways to complete the test.
10. (a) 105 = 100000
(b) 10 · 9 · 8 · 7 · 6 = 30240
(c) 104 · 5 = 50000
(d) 2 · 9 · 8 · 7 · 6 = 6048 (Here, I first found the number of choices for the last digit.)
(e) 3 · 8 · 8 · 7 · 6 = 8064 (Here, I first found the number of choices for the last digit, then
moved to the first digit.)
11. (a) 12!
(b) P (12, 10)
12.
12!
3!3!2!
= 6652800
13. C(17, 4) = 2380
14. C(15, 3) · C(18, 5) = 3898440
15. (a) C(25, 5) = 53130
(b) C(19, 5) = 11628
(c) C(6, 2) · C(19, 3) = 14535
2