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how can i translate this sentence to a quantifier formula, when the universe - { o|o is a set }

Any master has as elements all and only sets which are not elements of themselves.

i know it starts of with an existential quantifier since its dealing with a specific object "master"

any feedback would be great.

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1 Answer 1

I think "any master" translates into $\forall$ masters.

If I had to answer this question, I think I would first try to translate "all and only sets which are not elements of themselves". To do that, I might (as a partial answer) try to translate "a set that is not an element of itself", "all sets which are not elements of themselves" and "only sets which are not elements of themselves". Then I would try to merge these three partial answers into the answer to the original question.

Edit: I think "all sets that are not an element of themselves" looks like this: $$ \{ S \mid  S \not\in S \} $$

Hope this helps!

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