Final answer:
The principle of autonomy is the ethical principle which supports a competent patient's decision to discontinue their cancer treatment, respecting their self-determination.
Step-by-step explanation:
The ethical principle that supports a competent client’s decision to discontinue their cancer treatment is the principle of autonomy. This principle recognizes the patient’s right to make decisions about their own health care based on their values and preferences. The nurse is respecting the client's autonomy by supporting the client's choice, thus acknowledging their right to self-determination in their treatment plan, despite the nurse's personal beliefs about continuing treatment. The principle of autonomy recognizes the client's right to make decisions about their own healthcare, even if the nurse may personally disagree. It is important for the nurse to respect the client's autonomy and provide support for their decision.