Definition of set containment Let $X$ and $Y$ be sets. Does "$X$ contains $Y$" mean $Y \subseteq X$ or $Y\in X$, or is it ambiguous?

The symbols $\subset$ and $\subseteq$ are used for sets which are subsets of another, which can also be described as containment. The former is used when the sets are not equal, the latter when they can be.
The symbol $\in$ is used for elements of a set, rather than whole sets. For example, you could say: $$y\in Y\subseteq X \implies y\in X$$
