Which of the following is part of the Federal court system?

The U.S. District Court is indeed a vital component of the Federal court system. It serves as the trial court of the federal judiciary, where federal cases are initiated and adjudicated. Each state has at least one U.S. District Court, and larger states may have multiple districts to handle the volume of federal cases. These courts have jurisdiction over a variety of cases, including those involving federal laws, constitutional issues, and disputes between states or international parties.

In contrast, the other options listed pertain to state court systems. The State Supreme Court is the highest court in a state and handles appeals from lower state courts. Local County Courts are typically responsible for handling various matters at the local level, such as traffic violations and small claims. Family Courts specifically deal with family law matters like divorce, child custody, and adoption, again functioning within state jurisdictions. The inclusion of the U.S. District Court underlines its role in enforcing and interpreting federal laws, distinguishing it from the state judicial structures represented by the other courts mentioned.