Final answer:
The Avoiding style of conflict seeks to deny or ignore conflict and is characterized by a lack of engagement. It's one of the five main styles of handling conflict and can become problematic if used excessively. So, the correct option is 1) Avoiding style.
Step-by-step explanation:
The conflict style that seeks to deny conflict is the Avoiding style. This approach to dealing with conflict involves withdrawing from the conflict altogether, not providing input or showing any concern for either self-interest or the interest of the other parties involved. It is characterized by a deliberate decision to not engage or confront the issue at hand. The Accommodating style is about giving in to the other's needs and desires while neglecting one's own, whereas the Compromising style seeks a middle ground, the Competing style is assertive and uncooperative, and the Collaborating style involves cooperating with the other party to understand their concerns and express your own to find a win-win solution. Karen Horney suggested that while these strategies can be helpful, they may become problematic and lead to alienation if used excessively or inappropriately.