Translate the following inference to logic notation: If Michael were an electrician, then it is cold. If it is cold, then Barbara is climbing a mountain. If Barbara climbs a mountain, then John is a soldier. If John were a soldier, then Michael is making tea. For all x, if x_20 makes tea, then x_20 is an electrician. Therefore Michael is making tea if and only if it is cold.
P(a) -> p. p -> q. q -> r. r -> Q(a). forall x: Q(x) -> P(x). Therefore Q(a) <-> p.