(very) simple proof of sets

Question

If you have two very simple sets $\{1,2\}$ and $\{2,1\}$ and you want to prove they are equal can you just say they are equal by definition and a simple observastion? Thanks

Answer 1

$A=B$ means $ [x\in A\iff x\in B]$. So you can say. But if you are too suspects about it. Then take elements of $A$ one by one ( there are just two) and see they are in alo $B$. Then do same thing for $B$