Translate the following inference to logic notation: For all x, if x_6 plays squash, then x_6 is an office clerk. For all x, if x_6 were an office clerk, then x_6 is happy. There is at least one x for which x_6 is happy if and only if x_6 will play squash. Therefore there is at least one x for which x_6 will play squash if and only if x_6 is happy.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: R(x) <-> P(x). Therefore exists x: P(x) <-> R(x).