Translate the following inference to logic notation: If Charles takes a plane, then John is playing a game. For all x, x is a scientist or x will take a plane. Patricia is excited if and only if John is playing a game. If Charles were a scientist, then John is playing a game. Therefore Patricia is excited.
P(a) -> p. forall x: Q(x) or P(x). q <-> p. Q(a) -> p. Therefore q.