Comp232 - Mathematics For Computer Science - Ali Moallemi, Iraj Hedayati - Concordia University Page 17
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18Exercise 32
Show that the equivalence p
p
F can be derived using resolution
together with the fact that a conditional statement with a false hypothesis
is true. [Hint: Let q = r = F in resolution.]
Answer:
Resolution: ((p
q)
( p
r))
(q
r)
Let q = r = F , then:
((p
F )
( p
F ))
(F
F )
Hence,
(p
p)
F
To make above conditional statement true, hypothesis should be false,
p
p
F
Ali Moallemi, Iraj Hedayati
COMP232 - Mathematics for Computer Science
17 / 18
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