Local and global model checking are two algorithms that solve the same problem. Hence, if one of the two already gives us an answer, then that answer is the answer, and there is no need to re-check this with the alternative algorithm.

However, while that is true from a practical point of view, it still makes sense to ask for both in exam papers. Clearly, the answers for the two algorithms should also there be the same, but we just want to see that you are able to answer the same problem with the different approaches.

Note also that global model checking computes ALL states satisfying a property, while with local model checking, we are just checking that ONE state satisfies a property, which makes the two approaches a bit different.