We can see in the Venn diagram that an outcome is either in the blue region of A or in the white region of A, but it cannot be in both at the same time. We know that two events are disjoint if the occurrence of both events at the same time is impossible. Since there are no favorable outcomes that satisfy both A and A, the events are disjoint.
Example
To write examples, think of anything that has multiple possible outcomes. Make the event be any one of those outcomes. The complement will then be every other option possible outcome. Let's write some events!
A
A
Rolling a 6 on a die.
Rolling a number other than 6 on a die.
The Patriots win the Super Bowl.
Any other team wins the Super Bowl.
There is a surprise quiz on Wednesday.
There is a surprise quiz on Monday, Tuesday, Thursday, or Friday.
