Unformatted text preview: refore, x P(x).
(c is a particular
member of the domain.) premises
true
conclusion
true P(c)
x P(x) Existential generalization
24 Rules of inference for quantified
statement (example)
State which rule of inference is applied in the following
argument.
His dog is playing in the park.
Therefore, There is a dog playing in the park.
Solution:
Determine individual propositional function
P(x): x is playing in the park.
Domain: all dogs
Determine the argument using P(x)
P(his dog).
P(c)
Therefore, x P(x).
x P(x)
Domain: all dogs
25 Rules of inference for quantified
statement (example)
Show if x (P(x) Q(x)) is true, then x P(x)
true. (using direct technique)
Solution:
Assume x (P(x) Q(x)) is true.
Let a be some element of the domain,
that P(a) Q(a) is true.
So, P(a) is true and Q(a) is true.
So, x P(x) is true and x Q(x) is true.
Thus, x P(x)
x Q(x) is true x Q(x) is x P(x)
P(c)
P(a)
x P(x) 26 Rules of inference (example)
Show the following argument is valid.
Every one in this class has taken a course in co...
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 Summer '09
 Shafiei
 Computer Science, Logic, Ali, Personal computer

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