Consider the following premises. Thomas is bored if and only if Karen is a janitor. It is sunny if and only if Karen is a janitor. It is not sunny. For all x_7, x_7 is a nurse if and only if x_7 is bored. Can we infer the following from them? Thomas is a nurse.
 From the fact that it is sunny if and only if Karen is a janitor, and that it is not sunny we can infer that Karen is not a janitor. From the fact that for all x_7, x_7 is a nurse if and only if x_7 is bored we can infer that Thomas is a nurse if and only if Thomas is bored. From the fact that Thomas is bored if and only if Karen is a janitor, and that Karen is not a janitor we can infer that Thomas is not bored. Finally, from the fact that Thomas is a nurse if and only if Thomas is bored, and that Thomas is not bored we can infer that Thomas is not a nurse, which contradicts that Thomas is a nurse. Therefore, the answer is no.