Hey all, how can we prove the following proposition about set theory?

Let A,B,C be sets.

If A=B and B=C then A=C

Thanks!

Printable View

- Oct 22nd 2011, 01:32 PMjstarks44444Set Theory Transitivity Proof
Hey all, how can we prove the following proposition about set theory?

**Let A,B,C be sets.**

If A=B and B=C then A=C

Thanks! - Oct 22nd 2011, 03:23 PMMonroeYoderRe: Set Theory Transitivity Proof
Use the fact that $\displaystyle A=B \Leftrightarrow (A\subseteq B \text{ and } B\subseteq A)$

Then start by letting some $\displaystyle x\in A$ and you can show that $\displaystyle x\in C$

Then let some $\displaystyle y\in C$ and you can show $\displaystyle y\in A$