Translate the following inference to logic notation: For all x, x_3 will write a letter. For all x, x_3 will sleep if and only if x_3 will make tea. There is at least one x for which if x_3 makes tea, then x_3 is not writing a letter. Therefore there is at least one x for which x_3 will not sleep.
forall x: P(x). forall x: Q(x) <-> R(x). exists x: R(x) -> ~P(x). Therefore exists x: ~Q(x).