Final answer:
The core assumption of client-centered therapy relevant to the question is the unconditional positive regard from the therapist, which is fundamental in creating a supportive environment for the client.
Step-by-step explanation:
Among the three assumptions of client-centered therapy developed by Carl Rogers, unconditional positive regard from the therapist is a core concept. This principle is based on accepting and supporting the client regardless of what they say or do, fostering a nonjudgmental environment that encourages personal growth and self-discovery. Unlike directive approaches or interpretations that are characteristic of other forms of psychotherapy, client-centered therapy focuses on the client's own capacity to heal themselves with the support of these three critical elements: genuineness, empathy, and unconditional positive regard from the therapist.