Translate the following inference to logic notation: For all x, if x_7 were an electrician, then x_7 is playing a game. For all x, x_7 will play a game if and only if x_7 will write a letter. There is at least one x for which x_7 is an electrician. Therefore there is at least one x for which x_7 will play a game.
forall x: P(x) -> Q(x). forall x: Q(x) <-> R(x). exists x: P(x). Therefore exists x: Q(x).