Consider the following premises. Susan is a sailor if and only if John is a politician. John is not a politician. Susan is a sailor or Richard is cooking. John is a politician if and only if Susan is a sailor. Can we infer the following from them? Richard is cooking.
 From the fact that Susan is a sailor if and only if John is a politician we can infer that if Susan were a sailor, then John is a politician. From the fact that John is a politician if and only if Susan is a sailor we can infer that if John were a politician, then Susan is a sailor. From the fact that if Susan were a sailor, then John is a politician, and that if John were a politician, then Susan is a sailor we can infer that Susan is a sailor if and only if John is a politician. From the fact that Susan is a sailor if and only if John is a politician, and that John is not a politician we can infer that Susan is not a sailor. Finally, from the fact that Susan is a sailor or Richard is cooking, and that Susan is not a sailor we can infer that Richard is cooking. Therefore, the answer is yes.