这两个事件是独立发生的，没有任何关联。

These two events happened ___independently without any connection.

他独立完成了这个项目，没有寻求任何人的帮助。

He completed the project ___independently without seeking help from anyone.

她大学毕业后就独立生活了，不再需要父母的经济支持。

After college, she started living ___independently and no longer relied on her parents for money.

孩子们被鼓励独立思考解决问题。

Children are encouraged to solve problems ___independently.