Why Truth Tables We will learn several ways

Why Truth Tables? We will learn several ways to evaluate arguments for validity. * Proofs * Truth Tables * Trees

Why Truth Tables? There is no way to show that an argument is INVALID with the proof method.

Why Truth Tables? There is no way to show that an argument is INVALID with the proof method. Your failure to find a proof does not show an argument is INVALID.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F -P F T The truth value of -P is the opposite of the value of P.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F -P F T The truth value of -P is the opposite of the value of P. Dogs are mammals. Dogs are not mammals.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F -P F T The truth value of -P is the opposite of the value of P. Dogs are fish. Dogs are not fish.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P&Q T F F F The truth value of P&Q is T iff P is T AND Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F Pv. Q T T T F The truth value of Pv. Q is T iff P is T OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P<>Q T F F T The truth value of P<>Q is T iff the values of P and Q match.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P<>Q T F F T The truth value of P<>Q is T iff the values of P and Q match. Watch Out!

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T. The only F row

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T. If water is wet, then dogs are mammals.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T. If dogs are mammals, then dogs have hair.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T. If the moon is made of cheese, then some people are wrong.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T. If the moon is made of cheese, then the moon is edible.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T? T? F T? The truth value of P>Q is T iff P is F OR Q is T. If water is wet, then dogs are mammals.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T? T? F T? The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T.

Basic Truth Tables Truth tables tell us how to calculate truth values (T or F) of a complex statement give that we know the values of its parts. P T F Q T T F F P>Q T T F T The truth value of P>Q is T iff P is F OR Q is T. For more click here