Translate the following inference to logic notation: For all x, x_6 will write a letter or x_6 will sleep. For all x, x_6 is an office clerk or x_6 will not sleep. For all x, if x_6 writes a letter, then x_6 is an office clerk. There is at least one x for which x_6 will play tennis. Therefore there is at least one x for which x_6 is an office clerk and x_6 will play tennis.
forall x: P(x) or Q(x). forall x: R(x) or ~Q(x). forall x: P(x) -> R(x). exists x: S(x). Therefore exists x: R(x) and S(x).