Translate the following inference to logic notation: David is driving a car if and only if Mary is writing a letter. For all x, x_8 will sleep if and only if x_8 will drive a car. For all x, x_8 will not sleep. Therefore Mary is not writing a letter.
P(a) <-> p. forall x: Q(x) <-> P(x). forall x: ~Q(x). Therefore ~p.