Lets say you are given a bunch of statements and you need to ask some questions to prove them:(adsbygoogle = window.adsbygoogle || []).push({});

(a) How do you show that a set is a subset of another set.

I said to show that [itex] x\in A [/itex] and [itex] x\in B [/tex]. What else can you do to show what [itex] A\subset B [/itex]? Could you assume from the following: If [itex] A\cup B = B\cup A [/itex] then [itex] A\subset B [/itex]? (sorry, not experienced in set theory).

(b) If [itex] a [/itex] and [itex] b [/itex] are real nonnegative real numbers, then [itex] a^{2}+b^{2} \leq (a+b)^{2} [/itex]. Is this the Cauchy-Schwarz inequality? Basically, the questions that I ask in this case, is how can I prove that [itex] a^{2}+b^{2} \leq (a+b)^{2} [/itex] or [itex] (a+b)^{2}\geq a^{2}+b^{2} [/itex] and work from this (forward or backward)?

Thanks

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# Sets and Proofs

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