Consider the following premises. If Charles were a taxi driver, then Robert is a carpenter. Robert is a poet if and only if Charles is a taxi driver. If Robert were a carpenter, then Robert is a poet. Can we infer the following from them? Robert is a carpenter if and only if Charles is a taxi driver.
 From the fact that Robert is a poet if and only if Charles is a taxi driver we can infer that if Robert were a poet, then Charles is a taxi driver. From the fact that if Robert were a carpenter, then Robert is a poet, and that if Robert were a poet, then Charles is a taxi driver we can infer that if Robert were a carpenter, then Charles is a taxi driver. Finally, from the fact that if Robert were a carpenter, then Charles is a taxi driver, and that if Charles were a taxi driver, then Robert is a carpenter we can infer that Robert is a carpenter if and only if Charles is a taxi driver. Therefore, the answer is yes.