Consider the following premises. If Patricia plays squash, then Sarah is a sailor. For all z_2, if z_2 were a sailor, then z_2 is not climbing a mountain. For all z_2, z_2 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not playing squash.
 From the fact that for all z_2, if z_2 were a sailor, then z_2 is not climbing a mountain, and that for all z_2, z_2 will climb a mountain we can infer that for all z_2, z_2 is not a sailor via universal modus tollens. From the fact that for all z_2, z_2 is not a sailor we can infer that Sarah is not a sailor via universal instantiation. Finally, from the fact that if Patricia plays squash, then Sarah is a sailor, and that Sarah is not a sailor we can infer that Patricia is not playing squash via modus tollens. Therefore, the answer is yes.