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 INVALIDwith the proof method.

Why Truth Tables?

There is no way to show that an argument is INVALIDwith the proof method.

Your failure to find a proof does not showan argument is INVALID.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTF

-PFT

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) ofa complex statement give that we know the values of its parts.

PTF

-PFT

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) ofa complex statement give that we know the values of its parts.

PTF

-PFT

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) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P&QTFFF

The truth value of P&Q is T iffP is T AND Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

PvQTTTF

The truth value of PvQ is T iffP is T OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P<>QTFFT

The truth value of P<>Q is T iffthe values of P and Q match .

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P<>QTFFT

The truth value of P<>Q is T iffthe values of P and Q match .

Watch Out!

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP 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) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP 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) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP 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) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP 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) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP 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) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QT?T?FT?

The truth value of P>Q is T iffP 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) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QT?T?FT?

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

Basic Truth Tables

Truth tables tell us how to calculate truth values (T or F) ofa complex statement give that we know the values of its parts.

PTFTF

QTTFF

P>QTTFT

The truth value of P>Q is T iffP is F OR Q is T.

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