Comp232 - Mathematics For Computer Science - Ali Moallemi, Iraj Hedayati - Concordia University Page 18

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Exercise 33
Use resolution to show that the compound proposition
(p
q)
( p
q)
(p
q)
( p
q) is not satisfiable
Answer:
Resolution: ((p
q)
( p
r))
(q
r)
Let r = q, hence ((p
q)
( p
q))
(q
q), and
((p
q)
( p
q))
q
If hypothesis is TRUE, then q = TRUE.Therefor, either (p
q) or
( p
q) is FALSE.
On the other hand if hypothesis is FALSE, then the truth value of above
mentioned compound is FALSE.
Ali Moallemi, Iraj Hedayati
COMP232 - Mathematics for Computer Science
18 / 18

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