Consider the following premises. If Mary plays squash, then James is a carpenter. It is not overcast. Mary is playing squash if and only if it is snowing. It is snowing if and only if it is overcast. If James were a carpenter, then Mary is playing squash. Can we infer the following from them? James is not a carpenter.
 From the fact that it is snowing if and only if it is overcast, and that it is not overcast we can infer that it is not snowing. From the fact that if James were a carpenter, then Mary is playing squash, and that if Mary plays squash, then James is a carpenter we can infer that James is a carpenter if and only if Mary is playing squash. From the fact that James is a carpenter if and only if Mary is playing squash we can infer that if James were a carpenter, then Mary is playing squash. From the fact that Mary is playing squash if and only if it is snowing, and that it is not snowing we can infer that Mary is not playing squash. Finally, from the fact that if James were a carpenter, then Mary is playing squash, and that Mary is not playing squash we can infer that James is not a carpenter. Therefore, the answer is yes.