Translate the following inference to logic notation: There is at least one x for which x_5 is sad or x_5 will sleep. For all x, x_5 will not sleep or x_5 is a scientist. For all x, x_5 is not bored. For all x, x_5 is not sad or x_5 is bored. Therefore there is at least one x for which x_5 is a scientist.
exists x: P(x) or Q(x). forall x: ~Q(x) or R(x). forall x: ~S(x). forall x: ~P(x) or S(x). Therefore exists x: R(x).