Consider the following premises. Patricia is cooking if and only if William is an electrician. Patricia is cooking or David is not happy. Can we infer the following from them? The fact that David were happy does not imply that William is an electrician.
 From the fact that Patricia is cooking if and only if William is an electrician we can infer that if Patricia cooks, then William is an electrician. From the fact that Patricia is cooking or David is not happy we can infer that if David were happy, then Patricia is cooking. Finally, from the fact that if David were happy, then Patricia is cooking, and that if Patricia cooks, then William is an electrician we can infer that if David were happy, then William is an electrician, which contradicts that The fact that David were happy does not imply that William is an electrician. Therefore, the answer is no.