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Problem: $\sim$ is the mark for bijection between two set. Let $A$, $B$, $C$ be sets. Then$$A \sim A\\A\sim B \Rightarrow B\sim A\\(A\sim B \land B\sim C )\Rightarrow A\sim C$$ I know that is not a relation because it is define on set that contains all set which is not set. But my professor told that if I write like this it is OK.

Let $A,B,C\subset U$ where $U$ is some universal set. Then$$A \sim A\\A\sim B \Rightarrow B\sim A\\(A\sim B \land B\sim C )\Rightarrow A\sim C$$ Because I define relation $\sim$ on $P(U) × P(U)$ Is this correct?

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  • $\begingroup$ Yes, that's correct. $\endgroup$ – Floris Claassens Mar 19 at 11:38
  • $\begingroup$ It is a relation on $\wp(U)$ or equivalently a subset of $\wp(U)\times\wp(U)$. $\endgroup$ – drhab Mar 19 at 11:41

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