For the following argument, how can I produce an adequate translation, including interpretations function and formal sentence where universe $\mathcal{U} = \{\bigcirc\mid\bigcirc\text{ is a set}\}$.

And we can probably use:

M1: and o is a master set e: elements

1.) Any master set has as elements all and only set which are not elements of themselves.

2.) There are no master sets

and we can probabloy use: M1: and o is a master set e: elements

Am I on the right track?

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  • $\begingroup$ did you not ask this question here already math.stackexchange.com/questions/24972/quantifier-translation $\endgroup$ – Rudy the Reindeer Mar 4 '11 at 19:10
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    $\begingroup$ So far, your questions are obscurely and poorly worded, which is probably why you are not really getting much in the way of help. Try to spend some more time giving context, nomenclature, and explaining your thoughts so far. Extra time spent on formatting and correct spelling are a plus. $\endgroup$ – Arturo Magidin Mar 4 '11 at 19:16

I think you are asking: "How can I translate these sentences into formal ones using quantifiers?" Using $x\in M$ to mean "x is a master set", we'd get:

  1. $\forall x\in \mathcal{U}:x\in M \implies \forall y\in x: y\not\in y$
  2. $\neg\exists x\in \mathcal{U}: x\in M$

I'm not entirely sure what you mean by an interpretation function, but if you're just trying to generate an extension for these propositions, I think you can come up with some examples. Without knowing your universe though, I don't think we can do much to help.

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