Logic Test #1
Spring 2003
Professor Amy Kind
This test is open book and open notes/handouts, but closed neighbor. Computers are not
allowed. You may not share materials with one another during the test. Please be sure that all
answers are in your blue book. Partial credit will be given where appropriate.
I. Symbolizations (10 points each)
Using the translation scheme provided, translate the following five sentences into the language of
propositional (sentential) logic.
P:
Q:
R:
S:
Charlie buys a Wonka bar
Veruca buys a Wonka bar
Charlie finds a golden ticket
Veruca finds a golden ticket
T: Charlie is spoiled
U: Veruca is spoiled
W: Charlie is rich
X: Veruca is rich
Y: Veruca wins the chocolate factory
Z: Veruca is a kid
(Veruca is a female name)
1. Veruca, who found a golden ticket, wins the chocolate factory if and only if she is unspoiled.
2. Charlie bought a Wonka bar, but his doing so was not sufficient for his finding a golden
ticket.
3. Despite being a spoiled rich kid, Veruca will not find a golden ticket unless she buys a
Wonka bar.
4. If Veruca’s being unspoiled is necessary for her to win the chocolate factory, then she does
not win the chocolate factory.
5. Exactly one of Charlie and Veruca is spoiled, assuming that each of them is spoiled only if he
or she is rich.
II. Derivations (10 points each)
Using only the 10 primitive rules of Chapter One, provide a derivation of each of the following
five sequents. Please write each derivation on a separate page.
6.
P  ~T, Q  S, P & U, Q & U  R |- S  T  R
7.
R  P, T & S  R, ~Q  (~P  ~S), (P  R)  Q & S |- ~T
8.
P  R, S & (Q  T), Q  S & R |- P  T
9.
~(Q  T)  W, R  P  ~S, R  ~T, S  Q |- R  W
10.
S  P  S, P  R, P  T & Q, Q  R |- R & (S  T)