Unformatted text preview: (x) Q(x)) is true.
If a is in the domain then P(a) Q(a) is true.
So, P(a) is true and Q(a) is true.
Element a can be any element in the domain.
So, x P(x) is true and x Q(x) is true.
Thus, x P(x)
x Q(x) is true. x P(x)
P(a)
P(a)
x P(x) 21 Rules of inference for quantified
statement
Argument:
There is a fish in the pool.
Therefore,
some fish c in the pool.
x P(x).
Therefore, P(c).
(c is some member of
the domain.) premises
true
conclusion
true x P(x)
P(c) Existential instantiation
22 Rules of inference for quantified
statement (example)
State which rule of inference is applied in the following argument.
There is a person in the store.
Therefore, some person c is in the store.
Solution:
Determine individual propositional function
P(x): x is in the store.
Domain: all people
Determine the argument using P(x)
x P(x).
x P(x)
Therefore, P(c).
P(c)
Domain: all people
(c is some element of the domain.)
23 Rules of inference for quantified
statement
Argument:
George is in the pool.
Therefore,
there is a person in the pool.
P(c).
The...
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 Summer '09
 Shafiei
 Computer Science, Logic, Ali, Personal computer

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