# Two questions about Nash Equilibrium

I'm reading an introductory book on game theory, but I'm confused by Nash Equilibrium, can someone explain to me the following questions?

1. Will the iterated elimination of strictly dominated strategies eliminate a strategy that is part of a Nash Equilibrium, why?

2. For each player, will the utility of an equilibrium outcome always be better than the security level? If so, how to prove it?

Any idea will be appreciated, thanks a lot!