First Symbolic Exercises

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Presentation transcript:

First Symbolic Exercises P v Q 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. (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)]