Translate the following inference to logic notation: There is at least one x for which x_8 will play squash if and only if x_8 is bored. For all x, x_8 will play squash or x_8 is not bored. Therefore there is at least one x for which x_8 is bored if and only if x_8 will play squash.
exists x: P(x) <-> Q(x). forall x: P(x) or ~Q(x). Therefore exists x: Q(x) <-> P(x).