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I would say that only the empty graph is the correct solution, because if a structure is not empty then I can derive $\exists xR(x,x)$ from each of the given sentences.Show that the sentences $\forall x \exists y\forall z(R(x,y)\wedge R(x,z)\wedge R(y,z))$ and $\exists x\forall y\exists z(R(x,y)\wedge R(x,z)\wedge R(y,z))$ are not equivalent by exhibiting a graph that models one but not both of these sentences.