Final answer:
The type of insurance that would cover Dr. Dentem in a lawsuit for professional negligence is the Professional Liability Insurance option (3), which is designed to protect against claims stemming from professional services.
Step-by-step explanation:
The insurance that would cover the cost of the lawsuit against Dr. Dentem for administering too much laughing gas and causing brain damage is Professional Liability Insurance. This type of insurance is also known as malpractice insurance in the medical field, and it protects professionals against claims of negligence or harm due to professional services or advice.
General Liability Insurance typically covers bodily injuries or property damage, Property Insurance covers the physical property against damage or loss, and Workers' Compensation Insurance provides benefits to employees who get injured on the job.