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Unformatted text preview: li)
S(Ali)
Universal instantiation
C(Ali)
3. C(Ali)
Premise
4. S(Ali)
Modus ponens
So, the conclusion is true and the argument is valid.
29 Rules of inference (example)
Show the following argument is valid.
There is a student such that if he knows programming,
then he knows Java.
All students know programming.
Therefore, there is a student that knows either Java or
C++.
Solution:
Determine individual propositional function
P(x): x knows programming.
J(x): x knows Java.
C(x): x knows C++.
30 Rules of inference (example)
Show the following argument is valid.
There is a student such that if he knows programming, then he
knows Java.
All students know programming.
Therefore, there is a student that knows either Java or C++.
Solution:
Determine premises and the conclusion using P(x), J(x) and C(x)
P(x): x knows programming.
J(x): x knows Java.
C(x): x knows C++.
Premises:
x (P(x)
J(x))
domain: all students
x P(x)
Conclusion:
x (J(x) C(x))
31 Rules of inference (example)
Show the following argument is valid.
There is a student such that if he knows programming, then he knows
Java.
All students know programming.
Therefore, there is a student that knows either Java or C++.
Solution:
Assume premises are true, show the conclusion is true
1.
x (P(x)
J(x))
Premise
Premises:
2. P(a)
J(a)
Existential instantiation
x (P(x)
J(x))
3.
x P(x)
Premise
x P(x)
4. P(a)
Universal instantiation
5. J(a)
Modus ponens
6. J(a) C(a)
7.
x (J(x) C(x))
Existential generalization
32 Recommended exercises
2,3,8,9,19,23 33...
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 Summer '09
 Shafiei
 Computer Science

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