Translate the following inference to logic notation: For all x, x_7 will work if and only if x_7 will write a letter. For all x, x_7 will not work. For all x, if x_7 cooks, then x_7 is writing a letter. For all x, x_7 is a scientist if and only if x_7 will cook. Therefore for all x, x_7 is not a scientist.
forall x: P(x) <-> Q(x). forall x: ~P(x). forall x: R(x) -> Q(x). forall x: S(x) <-> R(x). Therefore forall x: ~S(x).