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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. - PowerPoint PPT Presentation
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p
r
rp
~
~
Is this a VALID ARGUMENT?
FF
TF
FT
TT
prrprp ~~
p
r
rp
~
~
Place truth values under the conclusion
TFF
TTF
FFT
FTT
prrprp ~~
p
r
rp
~
~
If there is a row T T Fit must be one of the first two rows
The conclusion is false only if p is true
T
T
false
TFF
TTF
FF
FT
prrprp ~~
p
r
rp
~
~
T
T
Now place truth values under the second premise.
T
T
false
If there is a row T T Fthen it must be the second row
TFF
TTF
FTF
FFT
prrprp ~~
p
r
rp
~
~
T
T
false
true
When the conclusion is false the secondpremise is true only if r is false
F
F
T
T
TFF
TTF
FT
FFTT
prrprp ~~
p
r
rp
~
~
T
T
false
trueF
F
We have eliminated all but one row in our search for the possibility T T F
In this case, we won’t find it because underthese conditions the first premise is false
F
false
FT
TFF
TTF
FT
FFTT
prrprp ~~
p
r
rp
~
~
T
T
false
trueF
F
F
false
FT
There are NO conditions under which the conclusion is false when the premises are true.If the premises are true then you must acceptthe conclusion.
VALID
Is this a VALID ARGUMENT?
qr
pr
qp
~
FFF
TFF
FTF
TTF
FFT
TFT
FTT
TTT
qrprqprqp ~
qr
pr
qp
~
Place truth values under the conclusion
TFFF
FF
TFTF
TTTF
TFFT
FT
TFTT
TTTT
qrprqprqp ~
qr
pr
qp
~T
T
T
T
F
F
F
F
false
The conclusion is false only whenr is true and q is false
TFFF
FF
TFTF
TTTF
TFFT
FT
TFTT
TTTT
qrprqprqp ~
qr
pr
qp
~T
T
T
T
F
F
F
F
false
Assign values to premise #1
TFFF
FFF
TFTF
TTTF
TFFT
FTT
TFTT
TTTT
qrprqprqp ~
qr
pr
qp
~T
T
T
T
F
F
F
F
false
Assign values to premise #1
TFFF
FFF
TFTF
TTTF
TFFT
FT
TFTT
TTTT
qrprqprqp ~
qr
pr
qp
~T
T
T
T
F
F
F
F
T
T
T
false
true
When the conclusion is false, the first premise is true only when p is true
TFFF
FFF
TFTF
TTTF
TFFT
FT
TFTT
TTTT
qrprqprqp ~
qr
pr
qp
~T
T
T
T
F
F
F
F
T
T
T
false
true
Ffalse
There are no conditions under which the conclusion is false and the premises are true.
VALID
Is this a VALID ARGUMENT?
r
qp
rp
FFF
TFF
FTF
TTF
FFT
TFT
FTT
TTT
rqprprqp
Place truth values under the conclusion
r
qp
rp
FFFF
TTFF
FFTF
TTTF
FFFT
TTFT
FFTT
TTTT
rqprprqp
r
qp
rp
The conclusion is false only if r is false
FFF
TTFF
FTF
TTTF
FFT
TTFT
FTT
TTTT
rqprprqp
r
qp
rp
The conclusion is false only if r is false
F
F
F
F
F
F
false
FFF
TTFF
FTF
TTTF
FFT
TTFT
FTT
TTTT
rqprprqp
r
qp
rp
F
F
F
F
F
F
Place truth values under premise #1
false
FTFF
TTFF
FTTF
TTTF
FFFT
TTFT
FFTT
TTTT
rqprprqp
r
qp
rp
F
F
F
F
F
F
When the conclusion is false premise #1 is true only when p is false
false
FTF
TTFF
FTT
TTTF
FFFT
TTFT
FFTT
TTTT
rqprprqp
r
qp
rp
F
F
F
F
F
F
When the conclusion is false premise #1 is true only when p is false
F
F
F
F
false
true
FTF
TTFF
FTT
TTTF
FFFT
TTFT
FFTT
TTTT
rqprprqp
r
qp
rp
F
F
F
F
F
F
F
F
F
F
false
true
If there is a row T T F then it is one of theyellow rows - complete them
FFTF
TTFF
FTT
TTTF
FFFT
TTFT
FFTT
TTTT
rqprprqp
r
qp
rp
F
F
F
F
F
F
F
F
F
F
false
true
If there is a row T T F then it is one of theyellow rows - complete them
T
T
true
FFTF
TTFF
FTT
TTTF
FFFT
TTFT
FFTT
TTTT
rqprprqp
r
qp
rp
F
F
F
F
F
F
F
F
F
F
false
true
T
T
true
There are conditions under which the premisesare true but the conclusion is false.
invalid
r
rs
rp
sq
qp
~
The conclusion is FALSE only if r is F
F
F
F
false
r
rs
rp
sq
qp
~Under these conditions, this premise is TRUE only if p is T
F
F
FT
T
false
true
r
rs
rp
sq
qp
~
Under these conditions, this premise is TRUE only if q T
F
F
FT
T T
T
false
true
true
r
rs
rp
sq
qp
~
Under these conditions, this premise is TRUE only if s is F
F
F
FT
T T
T
F
F
false
true
true
true
r
rs
rp
sq
qp
~ Under these conditions, this premise is FALSE
F
F
FT
T T
T
F
FF
false
true
true
true
r
rs
rp
sq
qp
~
F
F
FT
T T
T
F
FF
false
true
true
true
false
It is not possible for
all of the premises to be
true when the conclusion
is false. This is a
valid argument.
