Having hard time solving the following:

1. Given $\displaystyle \kappa$ is a regular cardinal, for every $\displaystyle \lambda$<$\displaystyle \kappa$ we'll define E={$\displaystyle \alpha $ < $\displaystyle \kappa $ | cf$\displaystyle \alpha$ = $\displaystyle \lambda$}. Prove that every such set is stationary.
2. f: $\displaystyle \kappa$ -> $\displaystyle \kappa$ . Prove that C = { $\displaystyle \alpha$ < $\displaystyle \kappa$ | f|$\displaystyle \alpha$: $\displaystyle \alpha$->$\displaystyle \alpha$} is closed and unbounded.

Sorry for the mess, I have never used TEX before.

Thanks in advance, every help will be appreciated.