Mathematical Foundation of Computer Science

DHARM

134 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE

~ (((((X 12 ∧∧∧∧→ ∼X ) X ) 3 X )4 5X ) T)

T

∼ ∼H ∼T

H

∼J ∼H

∼M J

∼∼T

M

T

∼M ∼H

(open path)

(((((X 12 ∧∧∧∧X ) X ) 3 X )4 5X )

~T∼

(((X 12 ∧∧∧X ) X ) 3 X ) 4

MH→ ∼

((X 12 ∧∧X ) X ) 3

∼→TM

(X 12 ∧X )

∼→ ∼HT

MJ→

JH→ ∼

×

×

×

×

×
Fig. 5.30
In this example, we will also determine the interpretation for which the argument is
invalid. Since we know that an argument is invalid when true premise/s derives a false conclu-
sion.