Proof with Sets Example with Intersection and Union

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Proof with Sets Example with Intersection and Union

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Not the best way to present this stuff. This isn't set theory, this is logic. Every operation on sets at this level is simply a logical operation on some large universe containing the sets A, B, C (i.e. the union of A B and C) and in this universe, the set operations are just logic. If I use lowercase letters a, b, c to denote the proposition x is in A, x is in B, x is in C respectively, you are asking to prove (a & ( b | c )) -> ((a & b) | c ) where & means and and | means or. This logical proposition can be checked automatically by truth tables, or you can think about it a second.

This symmetry between elementary set operations and logic deceived mathematicians into thinking set theory was equivalent to pure logic until Russell came along.

annaclarafenyo

Great video! A succinct and elegant proof of showing set inclusion.

stevenzimmerman

Maybe there's a shortcut, but strictly speaking doesn't
(x is in A) *and* (x is in (B U C))
imply that
(x is in A and x is in B)
or
(x is in A and x is in C)?
Nevertheless, the result follows in a few more steps. Thanks

rosshenderson

why does the upside down capital "U" mean "and", and why does the rightside version mean "or"? Don't and/or only apply to the "v" and upside down "v" only? lol im getting confused with the pqr propositional statement part of DM.

dbuc

Very helpful but I think these proofs are lame-not you. Element chasing is lame. Are there better methods? Is it possible to work with logic like vel and upside down vel?

marianoapuya

Few minutes to my exam, thanks so much

godwinprecious

Hello, how do i find first four terms of the sequence defined by the formula bk = 1 + 2k, for all integers k ≥ 0.

cmcotrading

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