True or False? Answers/explanations have to be at least half page long

1. Consider a two person one-shot, simultaneous game.True or False:If a pair of strategies {x',y'} is a Nash equilibrium to a game, then this pair is also a dominant strategy equilibrium to the game.
2. True or False:For the utility functionU(w) = ln(w), the coefficient of absolute risk aversion decreases as wealth increases.