Translate the following inference to logic notation: For all x, x_7 is a lawyer and x_7 is an astronaut. For all x, x_7 is a lawyer if and only if x_7 is a carpenter. Therefore for all x, x_7 is a carpenter.
forall x: P(x) and Q(x). forall x: P(x) <-> R(x). Therefore forall x: R(x).