You ask the child for all their passwords and install a monitor on their computer for other activity. If the child is going to circumvent this by creating a fake account or lying to you about being on a social network then this law still won't help you. In order for a website to give you access to an account, you have to know that account exists.

Bottom line, monitoring your child is part of being a parent and there are already tools in place to help with this. As the saying goes Trust but verify.