Translate the following inference to logic notation: For all x, x_17 will not work. For all x, x_17 is an astronaut if and only if x_17 will work. It is cloudy. For all x, x_17 is an astronaut or x_17 will write a letter. Therefore James is writing a letter and it is cloudy.
forall x: ~P(x). forall x: Q(x) <-> P(x). p. forall x: Q(x) or R(x). Therefore R(a) and p.