Haemon argues that creon’s indifference to the opinions of his subjects will result in the loss of their respect for his leadership. this argument is an example of pathos ethos logos hamartia

Logos

Haemon's argument stated above is an example of Logos because he is basically making an appeal to logic; he seeks to persuade his hearer(s) by reason. Logos is one of Aristotle’s three "ingredients for persuasion", namely: Ethos, Logos and Patheos. They are otherwise called "Appeals".

The correct answer is:  [C]:  "logos" .

Note:  "logos" refers to an "appeal to logic" .   Haemon's argument (as described in the the question is such an appeal; since Haemon is using "logic"—or "reason" / to describe the results of what could happen.

Neither don’t use either