There are two ways:
#1 (Map): Go to the map and pay attention to the event marker. If the black part of it is highlighted, then it's a new/incomplete event.
If it's not highlighted, then it's the event you completed. If you played the event, but didn't complete it yet, it will likely still be highlighted.
You can also use the filters to see all new or completed events.
#2 (Pause Menu): Go to the pause menu (PS4: Options/X1: Menu/PC: Escape), then go to the Missions category, in here you'll be able to see which events you've completed, and which ones you didn't.
This should help you.
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