Comp232 - Mathematics For Computer Science - Ali Moallemi, Iraj Hedayati - Concordia University Page 15

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Exercise 26 (cont...)
Justify the rule of universal transitivity which states that if
x (P (x)
Q(x)) and x (Q(x)
R(x)) are true, the
x (P (x)
R(x)) is true, where the domains of all quantifiers are the
same.
Answer (cont...):
P (a)
Q(a)
1
Q(a)
R(a)
2
P (a)
Q(a)
Q(a)
R(a)
P (a)
R(a)
Hypothetical syllogism
x(P (x)
R(x))
Universal generalization
Ali Moallemi, Iraj Hedayati
COMP232 - Mathematics for Computer Science
15 / 18

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