Give Some Information on : Power Set

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Give Some Information on : Power Set

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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In mathematics, the power set (or powerset) of any set S, written , P(S), ℙ(S) ℘(S) or 2S, is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set.
2^s you mean

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he power set of {1,2,3,4} is {{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.
you just copied and pasted wiki
i am just reading it now
If we have a set {a,b,c}: Then a subset of it could be {a} or {b}, or {a,c}, and so on, And {a,b,c} is also a subset of {a,b,c} (yes, that's true, but its not a "proper subset") And the empty set {} is also a subset of {a,b,c} In fact, if you list all the subsets of S={a,b,c} you will have the Power Set of {a,b,c}: P(S) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} } Think of it as all the different ways you can select the items (the order of the items doesn't matter), including selecting none, or all.
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ur wlc ;)

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