Having hard time solving the following:

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

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

Thanks in advance, every help will be appreciated.