P(A) $\subset$ P(B) implies A $\subset $ B proof or disproof.
I have a strange feeling this is false but I do not know. Something to do with P(A) $\subset$ P(B) seems strange since P(B) is itself a powerself with P(A) being a subset.
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Presumably $P(A)$ means the power set of $A$, that is, the collection of all subsets of $A$, and not the probability of $A$? – Dilip Sarwate Feb 22 '14 at 03:11
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Think about what it says: every subset of $A$ is also a subset of $B$, does it imply that $A$ is itself a subset of $B$? – Vadim Feb 22 '14 at 03:14
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P(A) is power set. A is itself a subset of A. I suppose. Hmm.. – Adam Staples Feb 22 '14 at 03:15
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I know this has been asked before. Not finding it immediately. – Thomas Andrews Feb 22 '14 at 03:22
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$A\in P(A)\subset P(B)$ so $A\in P(B)$. That is, $A$ is a subset of $B$.
Hanul Jeon
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1A $\in$ P(A) $\subset$ P(B) implies A $\in$ P(B) so that A $\subset$ B. Okay that makes sense. Idky I wanted this to be false. – Adam Staples Feb 22 '14 at 03:21