Translate the following inference to logic notation: If Robert were sad, then Patricia is listening to a song. If Patricia listens to a song, then Robert is sad. For all x, if x_12 cooks, then x_12 is sad. Therefore if Robert cooks, then Patricia is listening to a song.
P(a) -> p. p -> P(a). forall x: Q(x) -> P(x). Therefore Q(a) -> p.