Translate the following inference to logic notation: There is at least one x for which x_10 will write a letter or x_10 will sleep. For all x, x_10 is not a janitor. For all x, if x_10 writes a letter, then x_10 is a janitor. Therefore there is at least one x for which x_10 will sleep or x_10 is bored.
exists x: P(x) or Q(x). forall x: ~R(x). forall x: P(x) -> R(x). Therefore exists x: Q(x) or S(x).