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

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Presentation on theme: "Why Truth Tables? We will learn several ways to evaluate arguments for validity. * Proofs * Truth Tables * Trees."— Presentation transcript:

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

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

4 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.

5 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. PTFPTF -P F T The truth value of -P is the opposite of the value of P.

6 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. PTFPTF -P F T The truth value of -P is the opposite of the value of P. Dogs are mammals. Dogs are not mammals.

7 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. PTFPTF -P F T The truth value of -P is the opposite of the value of P. Dogs are fish. Dogs are not fish.

8 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. PTFTFPTFTF QTTFFQTTFF P&Q T F The truth value of P&Q is T iff P is T AND Q is T.

9 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. PTFTFPTFTF QTTFFQTTFF PvQ T F The truth value of PvQ is T iff P is T OR Q is T.

10 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. PTFTFPTFTF QTTFFQTTFF P<>Q T F T The truth value of P<>Q is T iff the values of P and Q match.

11 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. PTFTFPTFTF QTTFFQTTFF P<>Q T F T The truth value of P<>Q is T iff the values of P and Q match. Watch Out!

12 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T.

13 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T. The only F row

14 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. PTFTFPTFTF QTTFFQTTFF P>Q 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.

15 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. PTFTFPTFTF QTTFFQTTFF P>Q 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.

16 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. PTFTFPTFTF QTTFFQTTFF P>Q 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.

17 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. PTFTFPTFTF QTTFFQTTFF P>Q 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.

18 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T.

19 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. PTFTFPTFTF QTTFFQTTFF P>Q 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.

20 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. PTFTFPTFTF QTTFFQTTFF P>Q T? F T? The truth value of P>Q is T iff P is F OR Q is T.

21 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T.

22 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T.

23 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T.

24 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T.

25 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T.

26 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. PTFTFPTFTF QTTFFQTTFF P>Q T F T The truth value of P>Q is T iff P is F OR Q is T. For more click here

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