Exercise 2.10. A poset (or partially ordered set) is a relation R which is reflexive, transitive, and antisymmetric: (i.e., (x, y) E R and (y, x) ER implies r =y). Prove that the following are posets: !! (i) R= {(A, B) E 2ª × 2R : A C B} (ii) R= {(x,y) ER × R: r < y}

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