Consider the following premises. Barbara is playing squash if and only if David is a carpenter. Thomas is a nurse if and only if Barbara is playing squash. Can we infer the following from them? The fact that Thomas were a nurse does not imply that David is a carpenter.
 From the fact that Barbara is playing squash if and only if David is a carpenter we can infer that if Barbara plays squash, then David is a carpenter. From the fact that Thomas is a nurse if and only if Barbara is playing squash we can infer that if Thomas were a nurse, then Barbara is playing squash. Finally, from the fact that if Thomas were a nurse, then Barbara is playing squash, and that if Barbara plays squash, then David is a carpenter we can infer that if Thomas were a nurse, then David is a carpenter, which contradicts that The fact that Thomas were a nurse does not imply that David is a carpenter. Therefore, the answer is no.