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I was wondering if statements that hold in general in set theory, such as De Morgan's Laws, always hold in propositional logic as well. If not, what are some examples of such statements that in the context of propositional logic fail to hold?

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The propositions of set theory are consequences of the axioms of set theory, as there are no rules of propositional logic that involve the symbols \epsilon, \cap, \cup. Standard set theory always uses the basic laws of propositional logic in order to make inferences from the set-theoretic axioms.

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  • $\begingroup$ So does that mean there are no such examples? $\endgroup$ – user19405892 Apr 21 '16 at 1:15
  • $\begingroup$ I can't see how there can be any $\endgroup$ – DanielWainfleet Apr 21 '16 at 1:22

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