Under what conditions may state law fail under the Supremacy Clause?

The correct answer is that state law may fail under the Supremacy Clause if it interferes with federal objectives. The Supremacy Clause, found in Article VI, Clause 2 of the U.S. Constitution, establishes that federal law takes precedence over state law when there is a conflict. This means that if a state law undermines or obstructs the goals of a federal statute or regulation, it can be declared invalid. Federal law is crafted to accomplish specific goals and purposes, and state law must align with these federal objectives to coexist legally.

In regard to the other options, while local laws can conflict with state laws, this does not concern the Supremacy Clause, which primarily deals with federal and state law relationships. The point about a law not being federally recognized is also less relevant in this context, as the focus is on existing federal laws and their interaction with state laws. Lastly, the timing of when the state law was created relative to a federal statute does not inherently affect its validity under the Supremacy Clause; it is the content and implications of the law that determine whether it conflicts with federal authority.