Consider the following premises. It is sunny if and only if it is snowing. It is not late. Barbara is cooking if and only if it is late. It is snowing if and only if Barbara is cooking. Can we infer the following from them? It is sunny.
 From the fact that Barbara is cooking if and only if it is late, and that it is not late we can infer that Barbara is not cooking. From the fact that it is snowing if and only if Barbara is cooking, and that Barbara is not cooking we can infer that it is not snowing. Finally, from the fact that it is sunny if and only if it is snowing, and that it is not snowing we can infer that it is not sunny, which contradicts that It is sunny. Therefore, the answer is no.