Is this a VALID ARGUMENT?

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# Is this a VALID ARGUMENT? - PowerPoint PPT Presentation

Is this a VALID ARGUMENT?. Place truth values under the conclusion. T. T. false. If there is a row T T F it must be one of the first two rows. The conclusion is false only if p is true. T. T. T. T. false. Now place truth values under the second premise. F. F. true.

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## Is this a VALID ARGUMENT?

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Presentation Transcript

T

T

false

If there is a row T T F

it must be one of the first two rows

The conclusion is false only if p is true

T

T

T

T

false

Now place truth values under the second

premise.

F

F

true

If there is a row T T F

then it must be the second row

When the conclusion is false the second

premise is true only if r is false

T

T

T

T

false

false

F

In this case, we won’t find it because under

these conditions the first premise is false

T

F

F

true

T

F

T

false

We have eliminated all but one row in our

search for the possibility T T F

T

F

false

F

true

T

F

F

T

false

VALID

There are NO conditions under which the

conclusion is false when the premises are true.

If the premises are true then you must accept

the conclusion.

F

T

T

F

F

T

false

F

T

The conclusion is false only when

r is trueand q is false

F

T

T

F

F

T

false

F

T

Assign values to premise #1

F

T

T

F

F

T

false

F

T

Assign values to premise #1

T

F

true

T

T

T

T

F

F

T

false

F

T

When the conclusion is false, the first premise

is true only when p is true

T

F

true

T

T

false

T

T

F

F

T

F

false

VALID

F

T

There are no conditions under which the

conclusion is false and the premises are true.

F

F

F

F

false

F

F

The conclusion is false only if r is false

F

F

F

F

false

F

F

Place truth values under premise #1

F

F

F

F

false

F

F

When the conclusion is false premise #1

is true only when p is false

F

F

true

F

F

F

F

false

F

F

F

F

When the conclusion is false premise #1

is true only when p is false

F

F

true

F

F

F

F

false

F

F

F

F

If there is a row T T F then it is one of the

yellow rows - complete them

F

F

true

F

T

F

true

F

F

false

F

F

T

F

F

If there is a row T T F then it is one of the

yellow rows - complete them

F

F

true

F

T

F

true

F

F

false

F

F

T

invalid

F

F

There are conditions under which the premises

are true but the conclusion is false.

F

F

The conclusion is FALSE only if

r is F

F

false

T

Under these conditions, this premise is TRUE only if

p is T

T

F

true

F

F

false

T

T

Under these conditions, this premise is TRUE only if

qT

true

T

T

F

true

F

F

false

T

T

true

F

T

T

F

true

Under these conditions, this premise is TRUE only if

s is F

F

F

true

F

false

F

T

T

true

F

T

Under these conditions, this premise is FALSE

T

F

true

F

F

true

F

false

F

T

T

It is not possible for

all of the premises to be

true when the conclusion

is false. This is a

valid argument.

true

F

T

false

T

F

true

F

F

true

F

false