How to do proofs involving sets

Asked Jun 25 '16 at 22:18

Active Jun 25 '16 at 22:37

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I have just recently started preparing for a course I will be taking next year, but I have very limited knowledge as it relates to proofs. It seems as though the only proofs I am slightly familiar with are proofs by induction. I was wondering if there is a systematic way to approaching proofs and if there are any "rules," as silly as that may sound. As for my specific question, I stumbled upon this:

Let A be a set.

$\emptyset \in A \Rightarrow \exists B \hspace{2 mm} s.t. \hspace{2 mm} A = \wp (B)$

Determine, with proof, if the above statement is true.

edited Jun 25 '16 at 22:37

Matthew Conroy

11,234

asked Jun 25 '16 at 22:18

HASSOUN

1

I'm having trouble reading what the problem is asking. Could you rewrite or rephrase it? – change_picture Jun 25 '16 at 22:20
Done. First time using this – HASSOUN Jun 25 '16 at 22:29
I'm not sure what that symbol is supposed to be when you say A = ?(B). Could you clarify? – change_picture Jun 25 '16 at 22:35
It is the power set symbol. \wp – HASSOUN Jun 25 '16 at 22:35
I don't know for sure, but this doesn't seem true. If $A = {\emptyset, x, y}$, then $A$ has 3 elements, but the power set of a finite set has a power of 2 elements. – Jeff L. Jun 25 '16 at 22:43
You got it @HASSOUN ! – change_picture Jun 25 '16 at 22:44
Sorry, I'm not quite sure what you mean @gorzardfu . Can you clarify? – HASSOUN Jun 25 '16 at 22:46
You're right @HASSOUN , the statement above is not true for the exact same reason you just said. A set being nonempty does not mean it is the power set of another set, and one reason is because, as you stated, power sets must have cardinality 2^n where n is a natural number including possibly 0. – change_picture Jun 25 '16 at 22:49
Would that be considered a "proof"? – HASSOUN Jun 25 '16 at 22:50

How to do proofs involving sets

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