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I am a student and I get confused in translating some sentence to logic assertion.

For example: Joe does not have a lawyer, i.e. is not a customer of any lawyer.

The right way to translate is:

"For all $p$, if $p$ is lawyer then Joe is not a customer of $p$"

or

"For all $p$, if $p$ is lawyer ∧ Joe is not a customer of $p$"

What the difference between these two clause?

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    $\begingroup$ The second one is not well-formed at all -- there's an "if" with no matching "then". $\endgroup$ – Henning Makholm Aug 2 '15 at 19:38
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If you are having problems with this sort of very very elementary point, that suggests you need to do some general homework (a one-off answer to this particular question won't get to the roots of your difficulty). Literally dozens of people have written excellent introductory logic books covering exactly this kind of thing, with detailed chapters on question of translation to and from ordinary language to regimented first-order formal languages. You need to be spending some time carefully reading the relevant chapters of such a book. If you are a student, get yourself to the library. It will be time well-spent.

I'd recommend, for example, the coverage in P-t-r Sm-th's Introduction to Formal Logic. Though having no access to a library is no excuse either, as various texts are available online. For example, Paul Teller's Formal Logic Primer is freely available from his website and is also very good on such questions of translation and the principles behind them.

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  • $\begingroup$ sorry professor i changed my opinion, actually self publicity is allowed here, can you please edit your post so that i retract my downvote? excuse me sir ..... $\endgroup$ – user153330 Feb 4 '16 at 22:46
  • $\begingroup$ can u forgive me sir ???? $\endgroup$ – user153330 Feb 5 '16 at 9:21

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