Consider the following premises. If it is cloudy, then Mary is not a police officer. For all y, if y drinks water, then y is an office clerk. Joseph is an office clerk if and only if it is cloudy. Mary is a police officer. Can we infer the following from them? If we can, name the inference rule being used: Joseph is drinking water.
 From the fact that if it is cloudy, then Mary is not a police officer, and that Mary is a police officer we can infer that it is not cloudy via modus tollens. From the fact that for all y, if y drinks water, then y is an office clerk we can infer that if Joseph drinks water, then Joseph is an office clerk via universal instantiation. From the fact that Joseph is an office clerk if and only if it is cloudy, and that it is not cloudy we can infer that Joseph is not an office clerk via biconditional elimination. Finally, from the fact that if Joseph drinks water, then Joseph is an office clerk, and that Joseph is not an office clerk we can infer that Joseph is not drinking water via modus tollens, which contradicts that Joseph is drinking water. Therefore, the answer is no.