Translate the following inference to logic notation: There is at least one x for which x is an astronaut if and only if x is an electrician. For all x, x is an electrician. For all x, x is a writer. Therefore there is at least one x for which x is a writer and x is an astronaut.
exists x: P(x) <-> Q(x). forall x: Q(x). forall x: R(x). Therefore exists x: R(x) and P(x).