c
Math 166 WIR, Spring 2011, Benjamin
Aurispa
Math 166 Week in Review 1 Answer Key
Sections L.1, L.2, and part of 1.1
1. (a) Yes
(b) No (Exclamation)
(c) Yes
(d) No (Command)
(e) No (Question)
(f) Yes
(g) No (Ambiguous)
2. (a)
(b)
i. (r ∧ p)∧ ∼ q
ii. ∼ (q ∧ p) ∨ (q ∧ r)
iii. (q∧ ∼ r) Y (r ∧ p)
i. Ben lives in Texas and is not taking a math or English class.
ii. Ben does not live in Texas and is either taking a math class or an English class (but not
both).
3. (a) The value of Coke stock did not rise today.
(b) Some students study for finals.
(c) No animals have four legs.
4. See Full Solutions for ALL steps.
(a) A tautology
p q p ∨ ∼ (q ∧ p)
T
T
T
T
F
T
F
T
T
F
F
T
(b) Neither a tautology nor a contradiction.
p q (p ∧ q) Y (p∨ ∼ q)
T
T
F
T
F
T
F
T
F
F
F
T
1
c
Math 166 WIR, Spring 2011, Benjamin
Aurispa
(c) Neither a tautology nor a contradiction.
p q r (p Y ∼ q)∧ ∼ r
T
T
T
F
T
T
F
T
T
F
T
F
T
F
F
F
F
T
T
F
F
T
F
F
F
F
T
F
F
F
F
T
(d) Neither a tautology nor a contradiction.
p q r (p Y r)∧ ∼ (q ∨ r)
T
T
T
F
T
T
F
F
T
F
T
F
T
F
F
T
F
T
T
F
F
T
F
F
F
F
T
F
F
F
F
F
5. (a) True
(b) True
(c) False
2
c
Math 166 WIR, Spring 2011, Benjamin
Aurispa
6. (a) True
(b) False
(c) True
(d) True
(e) True
(f) True
(g) False
(h) False
(i) False
(j) False
7. (a) {6}
(b) {9}
(c) {3, 6, 7}
(d) {1, 2, 4, 5, 6, 7, 8, 10}
(e) ∅
(f) 8
(g) 31
(h) No, not disjoint
8. (a) The set of students at TAMU who do not listen to both country and pop.
(b) The set of students at TAMU who do not listen to rock or who listen to pop.
(c) The set of students at TAMU who listen to country and pop but not rock.
(d) C ∪ P ∪ R
(e) (C ∪ R)c
(f) (R ∪ P ) ∩ C c
(g) R ∩ P c ∩ C c
3