Comp232 - Mathematics For Computer Science - Ali Moallemi, Iraj Hedayati - Concordia University Page 12
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18Exercise 24
Identify the error or errors in this argument that supposedly shows that if
x (P (x)
Q(x)) is true then x P (x)
x Q(x) is true.
1)
x (P (x)
Q(x)) Premise
Validity:
Valid
2)
(P (c)
Q(c)) Universal instantiation from 1
Validity:
Valid
3)
P (c) Simplification from 2
Validity:
Invalid
4)
x P (x) Universal generalization from 3
Validity:
Valid
5)
Q(c) Simplification from 2
Validity:
Invalid
6)
x Q(x) Universal generalization from 5
Validity:
Valid
7)
x P (x)
x Q(x) Conjunction from of 4 and 6
Validity:
Invalid (Error)
Ali Moallemi, Iraj Hedayati
COMP232 - Mathematics for Computer Science
12 / 18
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