What are the questions that determine the various infringement issues of any valid patent. Elaborate with cases.

Determining infringement issues of a valid patent involves analyzing several key questions to assess whether the accused product or process falls within the scope of the patent claims. These questions help evaluate whether the accused infringing activity meets the criteria for literal infringement, infringement under the doctrine of equivalents, or other relevant infringement theories. Here are the questions commonly considered in patent infringement cases, along with examples of cases illustrating these issues:

1. Does the Accused Product or Process Implement Each Element of the Claim Literally?:
   In cases of literal infringement, the accused product or process must embody each element of at least one claim of the asserted patent exactly as specified in the claim language. Literal infringement does not require any deviation or substantial difference from the claim elements. For example, in the case of Graver Tank & Mfg. Co. v. Linde Air Prods. Co., the Supreme Court held that if every element in the accused device is identical to the claim elements, literal infringement exists.

2. Are There Equivalents for Missing Elements in the Accused Product or Process?:
   Under the doctrine of equivalents, infringement may still be found even if the accused product or process does not literally implement each claim element. Instead, the accused product or process may infringe if it performs substantially the same function, in substantially the same way, to achieve substantially the same result as the patented invention. In the case of Warner-Jenkinson Co. v. Hilton Davis Chem. Co., the Supreme Court clarified the test for equivalence, emphasizing the importance of considering the function-way-result test.

3. Is There Direct Infringement or Inducement of Infringement?:
   Direct infringement occurs when a party performs all the steps of a patented method or uses a patented product without authorization. Inducement of infringement occurs when a party actively encourages or induces another party to infringe a patent. In the case of Commil USA, LLC v. Cisco Systems, Inc., the Supreme Court clarified the standard for proving inducement of infringement, emphasizing the need to establish knowledge of the patent and intent to induce infringement.

4. Is There Contributory Infringement?:
   Contributory infringement occurs when a party provides components, materials, or services that are specially designed or adapted for use in an infringing product or process, knowing or actively encouraging their use in infringement. In the case of Aro Mfg. Co. v. Convertible Top Replacement Co., the Supreme Court established the doctrine of contributory infringement, holding that selling components with the intent and knowledge that they will be used in an infringing manner can constitute contributory infringement.

By addressing these questions, courts can assess whether the accused product or process infringes the valid patent. These inquiries help ensure a thorough analysis of infringement issues, balancing the rights of patent holders with the need to encourage innovation and competition in the marketplace.