Consider the three sentences def Vx P(x, x) def 02Vxy (P(x, y) → P(y, x)) -> 3 x 2 (((x, y) ^ P(y, z) → P(x, z))) which express that the binary predicate P is reflexive, symmetric and transitive, respectively. Show that none of these sentences is semantically entailed by the other ones by choosing for each pair of sentences above a model which satisfies these two, but not the third sentence - essentially, you are asked to find three binary relations, each satisfying just two of these properties.