Consider the following premises. Patricia is not a scientist. Jennifer is running or Elisabeth is sleeping. If Jennifer goes running, then Patricia is a scientist. John is playing tennis or Elisabeth is not sleeping. If Patricia were a scientist, then Jennifer is running. Can we infer the following from them? John is playing tennis.
 From the fact that if Patricia were a scientist, then Jennifer is running, and that if Jennifer goes running, then Patricia is a scientist we can infer that Patricia is a scientist if and only if Jennifer is running. From the fact that John is playing tennis or Elisabeth is not sleeping we can infer that if Elisabeth sleeps, then John is playing tennis. From the fact that Patricia is a scientist if and only if Jennifer is running, and that Patricia is not a scientist we can infer that Jennifer is not running. From the fact that Jennifer is running or Elisabeth is sleeping, and that Jennifer is not running we can infer that Elisabeth is sleeping. Finally, from the fact that if Elisabeth sleeps, then John is playing tennis, and that Elisabeth is sleeping we can infer that John is playing tennis. Therefore, the answer is yes.