Recall that a problem is NP-complete if it is in NP and every problem in NP can be reduced to it in polynomial time. Start by proving that Vertex Cover is in NP.

Demonstrate a polynomial-time reduction from a known NP-complete problem (e.g., 3-SAT or Clique) to Vertex Cover. Show how an instance of the known problem can be transformed into an instance of Vertex Cover.

Prove the correctness of the reduction by showing that the original problem has a solution if and only if the constructed Vertex Cover instance has a solution. Ensure the reduction runs in polynomial time and that the size of the Vertex Cover instance is polynomially bounded by the original problem instance.