Consider the following premises. Thomas is a scientist or it is not raining. It is raining or Karen is playing squash. Thomas is a scientist if and only if Karen is playing squash. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not a scientist.
 From the fact that Thomas is a scientist or it is not raining we can infer that if it rains, then Thomas is a scientist via rewriting. From the fact that Thomas is a scientist if and only if Karen is playing squash we can infer that if Karen plays squash, then Thomas is a scientist via biconditional elimination. Finally, from the fact that if it rains, then Thomas is a scientist, that if Karen plays squash, then Thomas is a scientist, and that it is raining or Karen is playing squash we can infer that Thomas is a scientist via disjunction elimination, which contradicts that Thomas is not a scientist. Therefore, the answer is no.