Exercise 3.2 - Answers

1

(i)

It shows that the argument is valid (assuming, of course, that you have made no mistakes).

 
(ii)

Nothing. To conclude anything you need to go back to your interpretation and, in the case of each open branch in the tableau, check whether the unticked formulae are consistent, given what they mean. If there is any open branch where the unticked formulae are consistent, the argument is invalid. If in every case the unticked formulae are inconsistent, the argument is valid.

2

(i)

It shows that the argument is valid (assuming, of course, that you have made no mistakes).

 
(ii)

Nothing. To conclude anything you need to go back to your interpretation and check each structure which provides a counterexample to see whether, given what the sentence-letters mean, any of the structures are consistent i.e. represent a possibility. If any of the structures is consistent, then the original argument is invalid. If they are all inconsistent, the original argument is valid.

 

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