First Symbolic Exercises
PvQ
Kareem Khalifa
Department of Philosophy
Middlebury College
Exercise A2
• ~(London is the capital of England &
Stockholm is the capital of Norway)
• ~(T & F)
• ~(F)
• T
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
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
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
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
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
Exercise C4
•
•
•
•
~B & P
~T & P
F&P
F
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.
•Let Q = T.
–
–
–
–
(T v Q) & ~(Q v T)
T & ~(T)
T&F
F
•(P v T) & ~(T v P)
•T & ~(T)
•T & F
•F
• So the whole statement must be false.
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)]
FvT
T
Exercise D2
• Either Iran or Libya raises the price of oil.
• IvL
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
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)]