Translate the following inference to logic notation: If Barbara were a writer, then Robert is a poet. For all x, if x_11 were a poet, then x_11 is a janitor. If Robert listens to a song, then Barbara is a writer. For all x, if x_11 were a janitor, then x_11 is listening to a song. Therefore Robert is a poet if and only if Robert is listening to a song.
p -> P(a). forall x: P(x) -> Q(x). R(a) -> p. forall x: Q(x) -> R(x). Therefore P(a) <-> R(a).