 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2005/calculus-linear-algebra-discrete-mathematics-logic-and-proof-and-models-of-computation/7/a/solution

reflexivity: antisymmetry: transitivity: \forall x R (x, x), \forall x \forall y ((R (x, y) \land R (y, x)) \to x = y), \forall x \forall y \forall z ((R (x, y) \land R (y, z)) \to R (x, z)) .

A reflexive relation relates each element to itself. An antisymmetric relation forbids distinct elements from relating in both directions. A transitive relation contains every composite of two successive related pairs. Together these axioms define a partially ordered set.

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