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