Translate the following inference to logic notation: Karen is a scientist if and only if John is happy. For all x, if z_4 were a scientist, then z_4 is a poet. Karen is not a poet. For all x, if z_4 were a poet, then z_4 is a scientist. Therefore John is not happy.
P(a) <-> p. forall x: P(x) -> Q(x). ~Q(a). forall x: Q(x) -> P(x). Therefore ~p.