I have set to arrayText question , like the picture，

if i select Activities "Not2"， will the Dropdown elements of Status only show " In progress" and "Completed" ,and hide "Not started"

You cannot hide options in a select element, you can only remove them. So, I think you will need to insert two drop-downs in column-2 and display the appropriate one based on the answer in column-1.

thank for you reply ,tp,
Would you please give me an example ？ I do not know how to write..

I can't give an example without more information.

What LimeSurvey version?
How do you insert the dropdowns?
Can you attach a sample survey containing only that group?