3. Formalize the following arguments in L1 providing a suitable dictionary. Make your formalization as detailed as possible. If you find an ambiguity in the argument, explain it to justify your choice of formalization. Once formalized, say whether the argument is valid in propositional logic. If it is, provide a natural deduction proof. If it is not, provide a counterexample. (a) Ali is not happy if he's alone. But he's not alone. Therefore he's happy.
3. Formalize the following arguments in L1 providing a suitable dictionary. Make your formalization as detailed as possible. If you find an ambiguity in the argument, explain it to justify your choice of formalization. Once formalized, say whether the argument is valid in propositional logic. If it is, provide a natural deduction proof. If it is not, provide a counterexample. (a) Ali is not happy if he's alone. But he's not alone. Therefore he's happy.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:3. Formalize the following arguments in Li providing a suitable
dictionary. Make your formalization as detailed as possible. If
you find an ambiguity in the argument, explain it to justify
your choice of formalization.
Once formalized, say whether the argument is valid in
propositional logic. If it is, provide a natural deduction proof.
If it is not, provide a counterexample.
(a) Ali is not happy if he's alone. But he's not alone.
Therefore he's happy.
(b) If our observations are correct, matter is finitely divisble.
For matter is finitely divisible unless there are no atoms.
And there are atoms, provided our observations are
correct.
(c) It's not true that our beliefs about the external world are
unjustified. For if there is no knowledge of the external
world, our beliefs about it are still justified, or at least
they are rational. And if there is knowledge of the
external world our beliefs about it are justified.
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