Translate the following inference to logic notation: If Michael writes a letter, then Barbara is reading a book. For all x, if x_17 reads a book, then x_17 is sleeping. Barbara is sleeping if and only if Michael is writing a letter. Therefore if Barbara sleeps, then Barbara is reading a book.
p -> P(a). forall x: P(x) -> Q(x). Q(a) <-> p. Therefore Q(a) -> P(a).