Translate the following inference to logic notation: There is at least one x for which x_6 will read a book if and only if x_6 will cook. For all x, if x_6 drinks water, then x_6 is reading a book. For all x, if x_6 cooks, then x_6 is drinking water. Therefore there is at least one x for which x_6 will cook if and only if x_6 will read a book.
exists x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: Q(x) <-> P(x).