Translate the following inference to logic notation: For all x, x_13 is happy. There is at least one x for which x_13 is a cashier if and only if x_13 is a poet. For all x, x_13 is a cashier. Therefore there is at least one x for which x_13 is happy and x_13 is a poet.
forall x: P(x). exists x: Q(x) <-> R(x). forall x: Q(x). Therefore exists x: P(x) and R(x).