Translate the following inference to logic notation: For all x, x_13 will take a plane if and only if x_13 will play tennis. Thomas is playing tennis if and only if Karen is a doctor. For all x, x_13 will not take a plane. Karen is a doctor if and only if Linda is climbing a mountain. Therefore Linda is not climbing a mountain.
forall x: P(x) <-> Q(x). Q(a) <-> p. forall x: ~P(x). p <-> q. Therefore ~q.