Consider the following premises. If Mary were a lawyer, then Joseph is a mechanic. If it snows, then Mary is a lawyer. It is cloudy if and only if Joseph is a mechanic. It is not cloudy. Can we infer the following from them? If we can, name the inference rule being used: It is snowing.
 From the fact that it is cloudy if and only if Joseph is a mechanic, and that it is not cloudy we can infer that Joseph is not a mechanic via biconditional elimination. From the fact that if Mary were a lawyer, then Joseph is a mechanic, and that Joseph is not a mechanic we can infer that Mary is not a lawyer via modus tollens. Finally, from the fact that if it snows, then Mary is a lawyer, and that Mary is not a lawyer we can infer that it is not snowing via modus tollens, which contradicts that It is snowing. Therefore, the answer is no.