If the individual tickets are visible but you want to be able to modify them as a group, you could keep your checkbox representation of true/false and introduce a set of controls. These wouldn't represent the current state but rather work as actions to modify all the tickets (and you can see from looking at the individual tickets what the current states are).
Checking a checkbox in these bottom controls would check the respective checkboxes for all tickets. Likewise, unchecking one would uncheck for all tickets. You would need to 'reset' to go back to the original state.
But how do the users know which values have changed and their prior value?
Do they need all that information, particularly the prior value? They might only need to know which tickets have had values changed in some way.
Italics on the ticket name could be used to denote that a change has been made and is pending save. User testing would reveal if that is clear (alternatives could be a star symbol next to the ticket name, or a clearer 'modified' label).
A succinct summary of the changes made also alleviates some of the fear of dealing with large sets of elements. For example "2 tickets will be impacted by these changes"
A 'reset' action may be sufficient for them to go back to see previous values and recover from mistakes.
Another way you could go, maybe if you didn't want to see the individual tickets (or even if you did), is to use a feature of a UI component which is a bit less known: the 'indeterminate' state of the checkbox component. It's typically used to denote that the associated child elements vary, and can't be represented by either a true or false value alone.
So here, clicking a checkbox with an indeterminate state would change it to true (checked) and clicking once more would change it to false (unchecked). Resetting all changes would revert it back to indeterminate.
One thing to keep in mind as well if you intend to use it in a web interface:
The indeterminate state is visual only. The checkbox is still either checked or unchecked as a state. That means the visual indeterminate state masks the real value of the checkbox, so that better make sense in your UI! - css-tricks.com/indeterminate-checkboxes