Translate the following inference to logic notation: If Linda listens to a song, then Charles is reading a book. For all x, if x_10 were a lawyer, then x_10 is listening to a song. If Charles reads a book, then Linda is a lawyer. Therefore Linda is listening to a song if and only if Charles is reading a book.
P(a) -> p. forall x: Q(x) -> P(x). p -> Q(a). Therefore P(a) <-> p.