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I have been exploring more about set theory beyond my textbook and I have ran into something I couldn't explain. Can you use logical conjunction/disjunction on sets and are they the same as union/intersection?

A $\bigcap$ B

A $\wedge$ B

where A and B are sets. Are these equivalent? What does the disjunction or two sets mean?

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    Note that if $S$ is some set, then $\mathcal{P}(S)$, the union, intersection and complementation forms a Boolean algebra. Similarly, the set of propositions with $\lor$, $\land$ and $!$ forms a Boolean algebra which may be established to be isomorphic.2012-10-09
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    @Shahab I don't understand... for a discrete math course should I be expecting that?2012-10-09
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    I am not sure whether you have studied Boolean algebra, but if you haven't just note that there [is a transformation](http://planetmath.org/encyclopedia/RepresentingABooleanLatticeByFieldOfSets.html) which transforms conjunction/disjunction between propositions to union/intersection between sets nicely. This is really besides the point of your question and hence I included it just as a comment.2012-10-09

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