Translate the following inference to logic notation: Sarah is bored if and only if James is fast. If Michael sleeps, then James is fast. For all x, x_7 will play a game if and only if x_7 is an astronaut. Mary is an astronaut if and only if Michael is sleeping. Sarah is not bored. Therefore Mary is not playing a game.
p <-> q. r -> q. forall x: P(x) <-> Q(x). Q(a) <-> r. ~p. Therefore ~P(a).