(b) That's right. A sole trader is a person who owns and operates a business on their own. A business operated by a sole trader can be called a 'sole proprietorship'. A sole proprietorship gives the owner the complete right to decide by themselves how to run the business.

It also means that all the responsibilities associated with running the business belong to the sole proprietor.

If a business is to be owned by more than one person, it cannot be operated as a sole proprietorship: some other business structure will be needed.

In the circumstances he has explained, it may well be appropriate for Edward to begin operating as a sole trader.