Consider the following premises. For all x, x will climb a mountain or x will read a book. There is at least one x for which x will read a book if and only if x will cook. For all x, x will not climb a mountain. Can we infer the following from them? For all x, x will not cook.
 From the fact that for all x, x will climb a mountain or x will read a book, and that for all x, x will not climb a mountain we can infer that for all x, x will read a book. From the fact that there is at least one x for which x will read a book if and only if x will cook we can infer that there is at least one x for which if x reads a book, then x is cooking. Finally, from the fact that there is at least one x for which if x reads a book, then x is cooking, and that for all x, x will read a book we can infer that there is at least one x for which x will cook, which contradicts that For all x, x will not cook. Therefore, the answer is no.