Translate the following inference to logic notation: For all x, if x_10 writes a letter, then x_10 is sleeping. For all x, x_10 will read a book if and only if x_10 will write a letter. There is at least one x for which if x_10 sleeps, then x_10 is writing a letter. For all x, x_10 will read a book if and only if x_10 is a mechanic. For all x, x_10 is not a mechanic. Therefore there is at least one x for which x_10 will not sleep.
forall x: P(x) -> Q(x). forall x: R(x) <-> P(x). exists x: Q(x) -> P(x). forall x: R(x) <-> S(x). forall x: ~S(x). Therefore exists x: ~Q(x).