Assume $\{x\}$ is transitive. What can you say about $x$? 
Definition. A set $X$ is transitive if every element of $X$ is a subset of $X$.

Assume $\{x\}$ is transitive. What can you say about $x$?
I think, $x$ is the set of natural numbers.

HINT: The set $\{x\}$ is transitive if and only if each element of $\{x\}$ is a subset of $\{x\}$. The only element of $\{x\}$ is $x$, so if $\{x\}$ is transitive, then $x\subseteq\{x\}$. This means that if $y\in x$, then $y\in\{x\}$.


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*If there is a $y\in x$, what must it be equal to? This makes $x$ a very strange set; why?  

*If there is no $y\in x$, what is $x$? Is $\{x\}$ transitive in this case?

