reduction

1
reduction example
2
r q s
lt
lt
p r
( m p )
q
?
3
F
r q s
lt
lt
p r
( m p )
F
q
?
the only conditions under which the conclusion
is false
4
F
r q s
lt
lt
p r
( m p )
F
q
?
the only conditions under which the conclusion
is false
5
F
r q s
lt
lt
p r
( m p )
F
q
?
the only conditions under which the conclusion
is false
6
F
r q s
lt
F
lt
p r
T
F
( m p )
F
q
?
the only conditions under which the conclusion
is false
7
F
T
r q s
lt
F
T
lt
p r
the only condition under which this premise is
true
T
F
( m p )
F
q
?
the only conditions under which the conclusion
is false
8
F
T
r q s
lt
Be careful, there are two possibilities s
might be false or s might be true
F
T
lt
p r
T
F
( m p )
F
q
?
the only conditions under which the conclusion
is false
9
F
T
r q s
lt
Be careful, there are two possibilities s
might be false or s might be true There are two
rows of the truth table on which the conclusion
is false and premises 2 and 3 are true
F
T
lt
p r
true
T
F
( m p )
true
F
q
?
false
10
T
F
T
true
r q s
lt
Be careful, there are two possibilities s
might be false or s might be true There are two
rows of the truth table on which the conclusion
is false and premises 2 and 3 are true We are
interested only in the possibility that all
premises are true when the conclusion is false.
F
T
lt
p r
true
T
F
( m p )
true
F
q
?
false
11
T
F
T
true
r q s
lt
Be careful, there are two possibilities s
might be false or s might be true There are two
rows of the truth table on which the conclusion
is false and premises 2 and 3 are true We are
interested only in the possibility that all
premises are true when the conclusion is false.
F
T
lt
p r
true
T
F
( m p )
true
F
q
?
false
This argument is INVALID
WHEN IT IS POSSIBLE TO MAKE A PREMISE false OR
true , YOU MUST MAKE IT TRUE .
12
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