Translate the following inference to logic notation: There is at least one x for which if x_7 cooks, then x_7 is sleeping. For all x, x_7 will write a letter or x_7 will cook. For all x, if x_7 writes a letter, then x_7 is working. For all x, x_7 will work if and only if x_7 will sleep. Therefore there is at least one x for which x_7 will sleep.
exists x: P(x) -> Q(x). forall x: R(x) or P(x). forall x: R(x) -> S(x). forall x: S(x) <-> Q(x). Therefore exists x: Q(x).