“I stood and
applied logic to it. Had he taken a taxi home? Not the way he hated taxis.
What, as I had left him standing there, what had been his most burning desires?
That was easy. To shoot me, to sit down, and to drink beer. He couldn’t shoot
me because I wasn’t there. Where might he have found a chair?”
Let: A = He hates taxis
B = He’s drinking beer
C = I should look for a chair
N = I’m not there
H = He’s trying to shoot me
S = He’s sitting
T = He took a taxi
Represent
the following argument and prove the conclusion:
(1) Either he took a taxi or else he’s trying
to shoot me or else he’s sitting and drinking beer.
(2) He didn’t take a taxi if he hates taxis
and he’s not trying to shoot me if I’m not there.
(3) I’m not there and he hates taxis.
(4) I should look for a chair if he’s
sitting.
:. He’s
drinking beer and I should look for a chair.
Note: The
first premise can be parenthesized as “[Either he took a taxi or else (he’s
trying to shoot me or else (he’s sitting and drinking beer))].”
Solution:
(1) [T v (H v
(S & B))] Prem.
(2) (A → ~T)
& (~N → ~H) Prem.
(3) ~H & A Prem.
(4) S → C Prem.
∴ B & C
(5) A 3,
&-Elimination
(6) A → ~T 2,
&-Elimination
(7) ~T 5, 6
Modus Ponens
(8) H v (S
& B) 1, 7
Disjunctive Syllogism
(9) ~H 3,
&-Elimination
(10) S & B 8, 9
Disjunctive Syllogism
(11) S 10,
&-Elimination
(12) C 4,
11 Modus Ponens
(13) B 10,
&-Elimination
(14) B & C 12,
13 &-Introduction 
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