Consider the following premises. For all z, z will climb a mountain if and only if z is a nurse. For all z, z is a nurse if and only if z will climb a mountain. Can we infer the following from them? There is at least one z for which if is not true that z is a nurse if and only if z will climb a mountain.
 From the fact that for all z, z will climb a mountain if and only if z is a nurse we can infer that for all z, if z climbs a mountain, then z is a nurse. From the fact that for all z, z is a nurse if and only if z will climb a mountain we can infer that for all z, if z were a nurse, then z is climbing a mountain. Finally, from the fact that for all z, if z were a nurse, then z is climbing a mountain, and that for all z, if z climbs a mountain, then z is a nurse we can infer that for all z, z is a nurse if and only if z will climb a mountain, which contradicts that There is at least one z for which if is not true that z is a nurse if and only if z will climb a mountain. Therefore, the answer is no.