First Symbolic Exercises

Kareem Khalifa

Department of Philosophy

Middlebury College

P v Q

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.

– (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

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

Exercise D2

• Either Iran or Libya raises the price of oil.

• I v L

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)]