No, you are definitely not asleep, though to an observer, you appear to be sleeping because you are in a state of deep physical relaxation. You are completely awake and aware of your surroundings. While in Trance, you are actually more alert and aware than you typically are in your normal waking state.
Author

Stielmond Ng, Principal Clinical Therapist
Master of Counselling (Monash University, Australia),
Principal Clinical Hypnotherapist,
Cognitive Behavioral Therapy (CBT) Practitioner,
Motivational Interview (MI) Practitioner.
Bachelor in Information Technology, (CQU).
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Absolutely not. You are always in control and fully aware of any suggestions given to you even when you are in trance. […]
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Quite the opposite! A gullible, unintelligent or weak-minded person is incapable of maintaining the necessary focus and concentration necessary to go into […]