Consider the following premises. For all z, z is not an astronaut. If Elisabeth were a scientist, then Karen is an astronaut. Elisabeth is a scientist if and only if Patricia is playing squash. Can we infer the following from them? Patricia is playing squash.
 From the fact that Elisabeth is a scientist if and only if Patricia is playing squash we can infer that if Patricia plays squash, then Elisabeth is a scientist. From the fact that for all z, z is not an astronaut we can infer that Karen is not an astronaut. From the fact that if Patricia plays squash, then Elisabeth is a scientist, and that if Elisabeth were a scientist, then Karen is an astronaut we can infer that if Patricia plays squash, then Karen is an astronaut. Finally, from the fact that if Patricia plays squash, then Karen is an astronaut, and that Karen is not an astronaut we can infer that Patricia is not playing squash, which contradicts that Patricia is playing squash. Therefore, the answer is no.