Translate the following inference to logic notation: There is at least one x for which x_7 will play a game if and only if x_7 will cook. For all x, x_7 is a janitor or x_7 is a taxi driver. For all x, if x_7 were a taxi driver, then x_7 is playing a game. For all x, x_7 is not a janitor or x_7 will cook. Therefore there is at least one x for which x_7 will play a game.
exists x: P(x) <-> Q(x). forall x: R(x) or S(x). forall x: S(x) -> P(x). forall x: ~R(x) or Q(x). Therefore exists x: P(x).