When booking or making an appointment form anything to stop doubles?

Hi, I'd like to know if making an appointment form for services when a person selects a time or date will that date then be occupied and non-useable. If two people went in and filled out for the 19th of Sept 2 1pm. Would one be rejected or be told that time is already taken? Needing a little more help with or if I can do that with JotForms. Would be great so I know at least I would not ever have double booking or appointment troubles. Thanks and look forward to the answer. To help a little more lets do carpet cleaning for the service. Usually I can't work but say three to four jobs a day. Each time slot is important so allowing a customer to know when appointments times are available or not would be great and helpful to them and also me.

We have a widget called Appointment Slots. Here's my demo form: https://form.jotform.com/62524225706957

I already signed up on the September 20, 2016 at 3:00 pm. So, it cannot be occupied now. If you're interested on my demo, please follow this steps:

1. Search for the Appointment Slots widget in the More Fields.

2. I added 3 Appointment Slots for September 20, 21 and 22.

3. Select the widget and then click the wand icon.

4. In the Appointment Slots widget, enter the available times in the Appointment times.

Hope that helps. Let us know if you need further help. Thank you.