Translate the following inference to logic notation: For all x, if x cooks, then x is reading a book. For all x, if x sleeps, then x is cooking. For all x, x is a writer if and only if x will sleep. There is at least one x for which if x reads a book, then x is happy. Therefore there is at least one x for which if x were a writer, then x is happy.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) <-> R(x). exists x: Q(x) -> T(x). Therefore exists x: S(x) -> T(x).