Consider the following premises. Barbara is running if and only if Linda is an electrician. David is drinking water or Michael is an office clerk. Linda is an electrician if and only if David is drinking water. Barbara is not running. Can we infer the following from them? If we can, name the inference rule being used: Michael is an office clerk or Joseph is cooking.
 From the fact that Barbara is running if and only if Linda is an electrician, and that Barbara is not running we can infer that Linda is not an electrician via biconditional elimination. From the fact that Linda is an electrician if and only if David is drinking water, and that Linda is not an electrician we can infer that David is not drinking water via biconditional elimination. From the fact that David is drinking water or Michael is an office clerk, and that David is not drinking water we can infer that Michael is an office clerk via disjunctive syllogism. Finally, from the fact that Michael is an office clerk we can infer that Michael is an office clerk or Joseph is cooking via addition. Therefore, the answer is yes.