1. First Symbolic Exercises
P v Q
Kareem Khalifa
Department of Philosophy
Middlebury College

2. Exercise A2
~(London is the capital of England & Stockholm is the capital of Norway)
~(T & F)
~(F) T

3. Exercise A8
(Paris is the capital of France & Rome is the capital of Spain) v (Paris is the capital of France & ~Rome is the capital of Spain)
(T & F) v (T & ~F)
(F) v (T & T)
(F) v (T) T

4. Lesson of this exercise
Sometimes you can save time in ascertaining the truth of a statement by looking at half of it.
(Paris is the capital of France & Rome is the capital of Spain) v (Paris is the capital of France & ~Rome is the capital of Spain)
This is true, so the whole thing is true

5. Exercise A14
~[~(~London is the capital of England & Rome is the capital of Spain) & ~(Rome is the capital of Spain & ~Rome is the capital of Spain)]
~[~(~T & F) & ~(F& ~F)]
~[~(F & F) & ~(F& T)]
~[~(F) & ~(F)]
~[ T & T ]
~[T] F

6. Exercise A21
~[~(Rome is the capital of Spain & Stockholm is the capital of Norway) v ~(~Paris is the capital of France v ~Rome is the capital of Spain)]
~[~(F & F) v ~(~T v ~F)]
~[~(F) v ~(F v T)]
~[ T v ~(T)]
~[ T v F]
~[T] F

7. Exercise A24
~[(~Rome is the capital of Spain v Stockholm is the capital of Norway) & ~(~Stockholm is the capital of Norway v Paris is the capital of France)]
~[(~F v F) & ~(~F v T)]
~[(T v F) & ~(T v T)]
~[(T) & ~(T)]
~[(T) & F]
~[F] T

8. Exercise C4
~B & P
~T & P
F & P F

9. Exercise C11 (P v Q) & ~(Q v P)
If the whole statement is true, then (P v Q) is true.
If (P v Q) is true, then either P or Q must be true.
Let P = T.
(T v Q) & ~(Q v T)
T & ~(T)
T & F F
So the whole statement must be false.
Let Q = T.
(P v T) & ~(T v P)
T & ~(T)
T & F F

10. Exercise C24 ~[~P v (~Q v A)] v [~(~P v Q) v (~P v A)]
~[~P v (~Q v T)] v [~(~P v Q) v (~P v T)]
~[~P v (T)] v [~(~P v Q) v (T)]
~[T] v [(T)]
F v T T

11. Exercise D2
Either Iran or Libya raises the price of oil.
I v L

12. Exercise D8
Either Saudi Arabia buys five hundred more warplanes and Iran raises the price of oil or Jordan requests more U.S. aid.
(S & I) v J

13. Exercise D22
Saudi Arabia buys five hundred more warplanes, and either Jordan requests more U.S. aid or both Libya and Iran raise the price of oil.
S & [J v (L & I)]