Translate the following inference to logic notation: For all x, if x_11 writes a letter, then x_11 is playing a game. For all x, x_11 is excited if and only if x_11 will play a game. For all x, if x_11 were excited, then x_11 is writing a letter. Therefore if Barbara were excited, then Barbara is writing a letter.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). forall x: R(x) -> P(x). Therefore R(a) -> P(a).