The only issue is whether or not your parents can claim you as a dependent. If they can, you must indicate that fact on your own tax return - whether they actually do claim you or not. And if they can claim you, you lose your own personal exemption. (Your parents would get your personal exemption on their return if they claim you.)
At age 20 and being a full-time student living with them, and with you almost certainly not providing more than half of your own support and you not filing a joint return with someone else, they certainly can claim you as a dependent.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
