Translate the following inference to logic notation: There is at least one x for which x_10 will make tea or x_10 is not fast. For all x, if x_10 makes tea, then x_10 is fast. For all x, if x_10 were fast, then x_10 is making tea. Therefore there is at least one x for which x_10 will make tea if and only if x_10 is fast.
exists x: P(x) or ~Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) <-> Q(x).