Translate the following inference to logic notation: If Michael were a mechanic, then James is sleeping. For all x, x will play squash if and only if x will sleep. If James plays squash, then Michael is a mechanic. Therefore James is playing squash if and only if James is sleeping.
p -> P(a). forall x: Q(x) <-> P(x). Q(a) -> p. Therefore Q(a) <-> P(a).