<P> The above two properties of an ordering are then axiomatized as: </P> <P> connectedness: For all (the objects of choice in the set) x and y, either x R y or y R x . </P> <P> transitivity: For all x, y, and z, x R y and y R z imply x R z . </P> <P> Thus, alternation (' or') and conjunction (' and') of R relations represent both the properties of an ordering for all the objects of choice . </P>

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