Comp232 - Mathematics For Computer Science - Ali Moallemi, Iraj Hedayati - Concordia University Page 8
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18Exercise 11
Show that the argument form with premises p
, p
, . . . , p and conclusion
1
2
q
r is valid if the argument form with premises p
, p
, . . . , p , q and
1
2
conclusion r is valid.
Answer:
It is sufficient to see that if (p
p
p )
(q
r) is false
1
2
then (p
p
p
q)
r is false.
1
2
Let (p
p
p )
(q
r) be false, then p
p
p is true
1
2
1
2
and q
r is false.
Moreover, for q
r to be false, q has to be true and r false.
So, p
, p
, . . . , p and q are true, and r is false.
1
2
Consequently, (p
p
p
q)
r is false.
1
2
Ali Moallemi, Iraj Hedayati
COMP232 - Mathematics for Computer Science
8 / 18
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