EDB — 24K

Exercises

1. [24K]Prerequisites:[23X]↺↻,[1Y5]↺↻,[224]↺↻. Given two relations \(a≤ b\) and \(a{\lt} b\) for \(a,b\in A\) show that these are equivalent:

   • \(a≤ b\) is a total order relation and

     \[ a{\lt}b = (a≤ b\land a\neq b)\quad , \]

   • \(a{\lt} b\) is an irreflexive, trichotomous and transitive relations and

     \[ a≤ b = (a{\lt} b\lor a= b)\quad . \]

   This latter \(a{\lt} b\) is called strict total order.