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.

Discrete Structures mathematics--- Which of the following is total order? ---{ <a,a>, <b,b>,<c,c>,<b,c>,<b,a>,<c,a> } ---{ &

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