Translate the following inference to logic notation: For all x, x_7 will make tea or x_7 is a police officer. There is at least one x for which x_7 will play tennis or x_7 will not make tea. For all x, x_7 will play tennis if and only if x_7 is a police officer. Therefore there is at least one x for which x_7 will play tennis.
forall x: P(x) or Q(x). exists x: R(x) or ~P(x). forall x: R(x) <-> Q(x). Therefore exists x: R(x).