I would like to determine the cardinality of the sets specified bellow. Nevertheless, I don't know how to approach or how to start such a proof. Any help will be appreciated.
If $X$ and $Y$ are well-ordered sets, then determine the cardinality of:
- $\{f : f$ is a function from $X$ to $Y\}$
- $\{f : f$ is an order-preserving function from $X$ to $Y\}$
- $\{f : f$ is a surjective and order-preserving function from $X$ to $Y\}$