Solu tion
R : Nixon is re-elected
L : Tulsa will lost its air base
V : Tulsa votes for Nixon
Given:
( )
( )
( )
1
2
3
¬ →
↔
¬ →





∴
R
L
R V
L R
Premises
R
(1) and (3) are equivalent.
(
) (
)
¬ →
∧
↔ ⇒
L R
R V
R
L
R
V (
)
¬ →
L R
(
)
R V
↔
(
)
¬ →
∧
L R
(
)
R V
↔
(
)
¬ →
∧
L R
(
)
R V
R
↔ ⇒
T
T
T
T
T
T
T
T
T
F
T
F
F
T
T
F
T
F
F
F
T
T
F
F
F
F
F
T
F
T
T
T
T
T
T
F
T
F
T
F
F
T
F
F
T
T
F
F
T
F
F
F
T
F
T
F
Therefore the given implication is “not a Tautology.” Therefore the argument
is not valid.
Ì Exam ple 8.2.8: For each of the following sets of premises, list the
relevant conclusions which can be drawn and the rules of inference used in
each case.
(a) I am either fat or thin, I’m certanly not thin.
(b) If I run I got out of breath. I’m not out of breath.
(c) If the butler did it, then his hands are dirty. The butler’s hands are
dirty.
(d) Blue skies make me happy and gray skies make me sad. The sky is
either blue or gray.
270
Theory of Automata, Formal Languages and Computation