Translate the following inference to logic notation: Sarah is reading a book. For all x, x_7 will not read a book or x_7 is an astronaut. For all x, x_7 will not sleep or x_7 is happy. Therefore there is at least one x for which x_7 is an astronaut or x_7 is happy.
P(a). forall x: ~P(x) or Q(x). forall x: ~R(x) or S(x). Therefore exists x: Q(x) or S(x).