4. [15%] If both a + b and ab are even, then both a and b are even. Prove or disprove the statement.

6. [15%] Which of the following graphs, K6 (complete graph with 6 vertices) or K7 (complete graph with 7 vertices) has closed Euler walk? Explain your answer as clear as possible. That is, in closed Euler walk, we allow each edge to be visited exactly once, and the initial vertex and ending vertex are the same. Can we modify the graph(s) to make it/them possible to contain a closed Euler walk?