Consider the following premises. Joseph is a sailor if and only if Patricia is a carpenter. Patricia is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not a sailor or it is cloudy.
 From the fact that Joseph is a sailor if and only if Patricia is a carpenter, and that Patricia is not a carpenter we can infer that Joseph is not a sailor via biconditional elimination. Finally, from the fact that Joseph is not a sailor we can infer that Joseph is not a sailor or it is cloudy via addition. Therefore, the answer is yes.