Translate the following inference to logic notation: For all x, x_12 is a mechanic if and only if x_12 will make tea. For all x, x_12 is excited if and only if x_12 will make tea. For all x, if x_12 were excited, then x_12 is a mechanic. Therefore for all x, if x_12 were a mechanic, then x_12 is excited.
forall x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). forall x: R(x) -> P(x). Therefore forall x: P(x) -> R(x).