For each of the following assertions, say whether it is true or false and support Your answer with examples or counterexamples where appropriate.

• For any local-search problem, hill-climbing will return a global optimum if the algorithm is run starting at any state that is a neighbor of a neighbor of a globally optimal state.

•Suppose the temperature schedule for simulated annealing is set to be constant up to time N and zero thereafter. For any finite problem, we can set N large enough so that the algorithm returns an optimal solution with probability 1.