You are generally considered single if you live alone, and cohabiting if you live with another person. 

However, the determining factor whether you are considered cohabiting (or not) is whether you have a shared household with another person. A shared household is when you collectively have financial and/or practical benefits that correspond to the benefits that married and cohabiting couples typically have.  

Financial benefits can be, for example, that you pay for expenses for daily consumption together or that you have regular ongoing expenses together. It can also be that you own real estate, a car, or other major financial investments together. 

Practical benefits can be, for example, taking turns shopping, cooking, doing laundry or regularly helping each other in similar ways. 

You can be cohabiting with a person you are not dating or married to. However, you cannot be cohabiting with your own children, grandchildren, siblings, or parents.

Here you can watch a short film about when you are considered single and cohabiting. Please note that the film is in Danish: