Consider the following premises. Joseph is a soldier if and only if it is late. Patricia is not cooking. It is cold if and only if it is late. Patricia is cooking if and only if Joseph is a soldier. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that Patricia is cooking if and only if Joseph is a soldier, and that Patricia is not cooking we can infer that Joseph is not a soldier via biconditional elimination. From the fact that Joseph is a soldier if and only if it is late, and that Joseph is not a soldier we can infer that it is not late via biconditional elimination. Finally, from the fact that it is cold if and only if it is late, and that it is not late we can infer that it is not cold via biconditional elimination, which contradicts that It is cold. Therefore, the answer is no.