Which amendment establishes that state and federal governments have different jurisdictions?

The Tenth Amendment is the correct answer because it explicitly delineates the distribution of powers between the federal government and the states. It states that any powers not delegated to the federal government by the Constitution, nor prohibited to the states, are reserved to the states or to the people. This indicates that states have their own jurisdiction that is separate from the federal government's powers. The Tenth Amendment is foundational in establishing federalism, wherein both levels of government operate independently within their respective spheres of authority.

The other amendments listed do not pertain to the division of jurisdiction between state and federal governments. The First Amendment focuses on individual rights such as freedom of speech, religion, and assembly; the Ninth Amendment addresses the rights retained by the people that are not specifically mentioned in the Constitution; and the Second Amendment guarantees the right to bear arms, with no reference to the division of governmental powers. Thus, it is the Tenth Amendment that correctly establishes the distinction between state and federal jurisdictions.