Solu tion
(a) F
F T
T
F
F T
T
F
P
P
:
( )
( )
( )
( ), (
I am fat
T :I am thin
∨
¬
∴
∨
¬
1
2
3
1 2
7
),
( ,
)
Dis. syll.
Q P Q P
∨ ⇒
Con clu sion: I am Fat
(b) R
B
R
B
B
R
R
B
B
:
:
( )
( )
( )
I run
I get out of breath
→
¬
∴→
¬
1
2
3 ¬
¬
→ ⇒ ¬
R
P
P
Q P Q
P
( ), ( ),
(
,
)
1 2 Mol - Tolens
Con clu sion: I did n’t run
(c) B : Butler did it
H: Hands are dirty.
B
H
H
→
Conclusion: Hypothesis
(d) B : Blue skies
H : Make me happy
G : Gray skies
S : Makes me sad
1.
B
H
→
P
2.
B G
∨
P
3.
B
(2), Sim pli fi ca tion
4.
H
(1), (3), Modus Ponens
5.
G S
→
P
6.
B G
∨
P
7.
G
(6), Sim pli fi ca tion
Con clu sion: I am either happy or sad.
Ì Exam ple 8.2.9: For each of the following set of premises, list the
relevant conclusions which can be drawn and the rules of inference used in
each case.
Prop o si tions and Pred i cates
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