Consider the following premises. Elisabeth is not playing squash. Karen is writing a letter if and only if Elisabeth is playing squash. It is sunny if and only if Karen is writing a letter. Can we infer the following from them? It is sunny.
 From the fact that Karen is writing a letter if and only if Elisabeth is playing squash, and that Elisabeth is not playing squash we can infer that Karen is not writing a letter. From the fact that it is sunny if and only if Karen is writing a letter we can infer that if it is sunny, then Karen is writing a letter. Finally, from the fact that if it is sunny, then Karen is writing a letter, and that Karen is not writing a letter we can infer that it is not sunny, which contradicts that It is sunny. Therefore, the answer is no.