Translate the following inference to logic notation: For all x, if x_10 writes a letter, then x_10 is playing a game. If Richard were a poet, then Jennifer is writing a letter. If Jennifer plays a game, then Richard is a poet. Therefore Jennifer is writing a letter if and only if Richard is a poet.
forall x: P(x) -> Q(x). p -> P(a). Q(a) -> p. Therefore P(a) <-> p.