Discrete Structures mathematics Which of the following is to
Discrete Structures mathematics---
Which of the following is total order?
---{ <a,a>, <b,b>,<c,c>,<b,c>,<b,a>,<c,a> }
---{ <a,a>, <b,b>,<b,c>,<c,c>, <d,d>,<c,b>}
---{ <a,a>, <b,b>,<c,c>, <d,d>,<b,a>,<a,c> }
---{ <a,b>, <b,c>, <a,c> }
Solution
First two satisfies all the conditions i.e reflexivity, antisymmetry, transitivity and comparability.
But third one fails to satisfy transitivity, because (b,a) is there and (a,c) is there so to satisfy transitivy it must have (b,c) which is not there
In fourth one, it fails to satify reflexivity.

