# Set notation “element-of” multiple sets

Let's say I have defined $X$ = users type x and $Y$ = users type y, and I would like to define $u$ is element-of $X$ and also element of $Y$, is there a simpler way to express, or the expression below is in the simplest form?

$$u =\{ e | e \in X \wedge e \in Y \}$$

Thank you.

Regards, Andy.

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You can say that $u = X \cap Y$. This should be the easiest standard way to use set notation to denote this.
so there is no such thing as {$e \in X,Y$} I supposed? – cherhan Dec 5 '11 at 5:19
It is not very convenient to use $\{ e \in X,Y \}$ is mathematics since the need to use the notation you suggested doesn't show up, the notation $X \cap Y$ is more suggestive and more compact, too. – Patrick Da Silva Dec 5 '11 at 5:21
When dealing with sets, it is customary to use capital letters for sets and lowercase letters for elements. So, if you want to denote the set of all elements that are members of both $X$ and $Y$, then $U = X \cap Y$ is more typical. If you mean to simply denote a single element that happens to belong to both $X$ and $Y$, then you would say $u \in X \cap Y$ (the $\in$ means "element of"). – Austin Mohr Dec 5 '11 at 8:14