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a. Let G be a graph with vertex set V = {2, 3, 4, 5, 6, 7, 8, 9} and let {i, j} be an edge if and only if i + j V. Does G have any loops?

b. Let G be a graph with vertex set V = {2, 3, 4, 5, 6, 7, 8, 9} and let {i, j} be an edge if and only if i j and there is a prime number that divides both i and j. Does G have any loops? Also find a path of longest length.