Which of the following is illegal when trapping fur-bearing mammals?

Setting a trap without registration is illegal when trapping fur-bearing mammals because regulatory bodies require trappers to register their traps to ensure compliance with local wildlife conservation laws. Registration helps monitor trapping activities, ensuring that they are conducted sustainably and in adherence to management objectives aimed at preserving fur-bearing species. This requirement also aids in tracking the number of traps in use, identifying potential over-harvesting of certain species, and maintaining public safety by minimizing unregulated trapping activities.

The other options listed, such as using non-lethal methods, visiting traps daily, and using traps in water, are permissible practices, provided they comply with specific guidelines and regulations in place to ensure humane treatment of animals and to minimize ecological impact.