Show-Hide actions will cause fields to display or disappear based on the registrant's selection. This video will show you how they work.  
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Note: The action will automatically assume the opposite is true. 

For example, if you tell an option to show based on a certain condition, it will automatically hide the rest of the time. 

As registrants register, deleting a field from the page will delete your registrant's information tied to that field. Instead of deleting, hide the field so you can still access the information as needed.

Here is how:

Create an action to hide the field after today's date.