Translate the following inference to logic notation: Thomas is cooking if and only if it is windy. For all x, x_13 will listen to a song if and only if x_13 will cook. It is windy if and only if it is raining. For all x, x_13 will not listen to a song. Therefore it is not raining.
P(a) <-> p. forall x: Q(x) <-> P(x). p <-> q. forall x: ~Q(x). Therefore ~q.