1. Definition: Mutual exclusion means that two events do not occur at the same time, that is, the intersection of A and B is an empty set, and mutual incompatibility is a stronger condition, that is, the two events are completely independent without any overlap.

2. Inclusion relationship: Mutual exclusion is a necessary condition for mutual incompatibility, but it is not a sufficient condition. In other words, if two events are incompatible with each other, then they must be mutually exclusive; But these two events are mutually exclusive, and they are not necessarily mutually exclusive.

3. Application scenario: The concepts of mutual exclusion and incompatibility are widely used in probability theory. The probabilities of mutually exclusive events can be added directly, and the probabilities of incompatible events need to be calculated by other methods.

4. Mathematical properties: Mutually exclusive and incompatible events have many similar properties in mathematics, such as union equals union, intersection equals intersection, and so on.

5. Practical significance: In practical application, the concepts of mutual exclusion and mutual incompatibility are helpful to better understand and analyze the relationship between events, so as to make more accurate predictions and decisions.