Translate the following inference to logic notation: For all x, x_6 is an astronaut or x_6 will sleep. For all x, x_6 will not sleep. There is at least one x for which x_6 will cook. For all x, x_6 is not an astronaut or x_6 will climb a mountain. Therefore there is at least one x for which x_6 will cook and x_6 will climb a mountain.
forall x: P(x) or Q(x). forall x: ~Q(x). exists x: R(x). forall x: ~P(x) or S(x). Therefore exists x: R(x) and S(x).