Final answer:
The formula A∪B−A∩B represents the union of two sets minus their intersection, which includes all elements in either set but not those common to both. In probability terms, when sets A and B are mutually exclusive, their union is the sum of their separate probabilities as they cannot occur simultaneously.
Step-by-step explanation:
Understanding Set Operations
The formula for the union minus the intersection in set theory is A∪B−A∩B. This operation effectively combines all the elements in sets A and B (A∪B) and then removes those elements that are common to both sets (A∩B). In our given example, the set A AND B (A∩B) contains the elements {14,16,18}, which are in both A and B. The set A OR B (A∪B) contains the elements {2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19}, which are in either set A or B or both. By subtracting the intersection from the union, we effectively remove the common elements from the combined set, therefore answer choice a) A∪B−A∩B is correct.
Mutually exclusive events in probability are such that the occurrence of one event excludes the occurrence of the other. When two events A and B are mutually exclusive, it is true that P(A AND B) = 0. The probability of either A or B occurring is the sum of their individual probabilities, P(A OR B) = P(A) + P(B). This principle is also seen in set theory, where two sets A and C that have no common elements are considered mutually exclusive, and their intersection is an empty set.