Translate the following inference to logic notation: For all x, x_11 is not a politician. For all x, x_11 is a politician if and only if x_11 will sleep. There is at least one x for which x_11 will sleep. Therefore there is at least one x for which x_11 will play tennis.
forall x: ~P(x). forall x: P(x) <-> Q(x). exists x: Q(x). Therefore exists x: R(x).