Final answer:
Mutual exclusivity in probability refers to events that cannot occur simultaneously, such as sets with an intersection of zero. Non-mutually exclusive sets do share elements, and the union of sets combines all unique elements from each set. This understanding assists in interpreting set operations like intersections and unions in problems.
Step-by-step explanation:
The question presented focuses on the concept of mutual exclusivity and union of sets within the context of probability theory. To address the student's question, we need to recognize that mutual exclusivity refers to the characteristic of two events that cannot occur at the same time. An intersection (denoted by P∩T) of two mutually exclusive sets should yield an empty set. Conversely, the union of sets (denoted by P∪T) entails combining all unique elements from both sets without duplication.
Based on the provided examples, we see that:
- Mutual exclusivity is demonstrated by the situation where P(C AND E) is zero, meaning there is no overlap between sets C and E.
- For sets that are not mutually exclusive, such as in P(A AND C), a nonzero probability indicates that some events are common to both sets.
- Union of sets, as demonstrated in P(C OR P), combines elements from both sets, leading to a larger set containing unique elements from the individual sets.