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The developmental tasks that involve establishing one's own life and setting one's own likes, dislikes, preferences, and beliefs is: Achieving autonomy and establishing identity.

Autonomy simply means to be independent or to have  freedom to choose what you like or dislikes without being control by others.

Achieving autonomy  is the ability of a person to achieve independent by choosing or going for what he or she want or desire or by choosing their own way of life.

Which means that  you can  tends to set your own principles, likes and dislikes, preference among others without anybody having to dictate for you or tell you what to do.

Establishing identity enables you to know your true self or your true identity.

Inconclusion the developmental tasks that involve establishing one's own life and setting one's own likes, dislikes, preferences, and beliefs is: Achieving autonomy and establishing identity.

Learn more about autonomy here:https://brainly.com/question/536789

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