Consider the following premises. If Sarah were a lawyer, then Joseph is playing tennis. Sarah is a lawyer if and only if Joseph is playing tennis. Can we infer the following from them? If is not true that Joseph is playing tennis if and only if Sarah is a lawyer.
 From the fact that Sarah is a lawyer if and only if Joseph is playing tennis we can infer that if Joseph plays tennis, then Sarah is a lawyer. Finally, from the fact that if Joseph plays tennis, then Sarah is a lawyer, and that if Sarah were a lawyer, then Joseph is playing tennis we can infer that Joseph is playing tennis if and only if Sarah is a lawyer, which contradicts that If is not true that Joseph is playing tennis if and only if Sarah is a lawyer. Therefore, the answer is no.