3. (10 points) Suppose is a set consisting of the following sentences. Is satisfiable? Justify your...
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3. (10 points) Suppose is a set consisting of the following sentences. Is satisfiable? Justify your answer. If is satisfiable, provide two structures that satisfy Þ. If it's not, present two sets of sentences which can be obtained by modifying and are satisfiable. Vryz(between(x, y, z)→ between(z, y, x)). VrVyz((between(x, y, z) A between(y, x, z)) → (x = y)). VrVyzw(between(y, z, z) → (between(y, x, w) V between (z, x, w))). Vryz(between(y, x, z) V between(z, y, z) V between(x, z, y)). VrVyz(between(x, y, z)→-between(y, x, z)). (1) (2) (3) (4) (5) 3. (10 points) Suppose is a set consisting of the following sentences. Is satisfiable? Justify your answer. If is satisfiable, provide two structures that satisfy Þ. If it's not, present two sets of sentences which can be obtained by modifying and are satisfiable. Vryz(between(x, y, z)→ between(z, y, x)). VrVyz((between(x, y, z) A between(y, x, z)) → (x = y)). VrVyzw(between(y, z, z) → (between(y, x, w) V between (z, x, w))). Vryz(between(y, x, z) V between(z, y, z) V between(x, z, y)). VrVyz(between(x, y, z)→-between(y, x, z)). (1) (2) (3) (4) (5)
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