Consider the following premises. It is not overcast. If Karen plays squash, then Elisabeth is a police officer. Elisabeth is a police officer if and only if it is overcast. If Elisabeth were a police officer, then Karen is playing squash. Can we infer the following from them? Karen is playing squash.
 From the fact that if Elisabeth were a police officer, then Karen is playing squash, and that if Karen plays squash, then Elisabeth is a police officer we can infer that Elisabeth is a police officer if and only if Karen is playing squash. From the fact that Elisabeth is a police officer if and only if it is overcast we can infer that if Elisabeth were a police officer, then it is overcast. From the fact that if Elisabeth were a police officer, then it is overcast, and that it is not overcast we can infer that Elisabeth is not a police officer. Finally, from the fact that Elisabeth is a police officer if and only if Karen is playing squash, and that Elisabeth is not a police officer we can infer that Karen is not playing squash, which contradicts that Karen is playing squash. Therefore, the answer is no.