![]() ![]() the probability that the student belongs to a club OR works part time.the probability that the student belongs to a club given that the student works part time.the probability that the student belongs to a club AND works part time.the probability that the student works part time.the probability that the student belongs to a club.The general terminology for the three areas of the Venn diagram in Figure 3.6 is shown in Figure 3.7. Translating the English word "AND" into the mathematical logic symbol ∩ ∩, intersection, and the word "OR" into the mathematical symbol ∪ ∪, union, provides a very precise way to discuss the issues of probability and logic. ![]() The values 10, 11, and 12 are part of the universe, but are not in either of the two sets. The symbol for the UNION is ∪ ∪, thus A ∪ B = A ∪ B = numbers 1-9, but excludes number 10, 11, and 12. These numbers are called the UNION of the two sets and in this case they are the numbers 1-5 (from A exclusively), 7-9 (from set B exclusively) and also 6, which is in both sets A and B. The number does not have to be in BOTH groups, but instead only in either one of the two. There are also those numbers that form a group that, for membership, the number must be in either one or the other group. The statement A ∩ B A ∩ B is read as "A intersect B." You can remember this by thinking of the intersection of two streets. The intersection is written as A ∩ B A ∩ B where ∩ ∩ is the mathematical symbol for intersection. All members that are part of both sets constitute the intersection of the two sets. This condition is called the INTERSECTION of the two sets. The English word "and" means inclusive, meaning having the characteristics of both A and B, or in this case, being a part of both A and B. Some number are in both sets we say in set A ∩ ∩ in set B. First, the numbers are in groups called sets set A and set B. Figure 3.6 shows the most basic relationship among these numbers. ![]()
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