Question

in a survey of 66 students, 17 said they were taking algebra and 49 said they were taking biology. are there necessarily 66 students taking algebra or biology? why? select the correct choice below. a. no, because the sets, represented by the class taken, are not necessarily disjoint. some students may be taking algebra and biology. b. no, because the sets, represented by the class taken, are disjoint, there is no way to determine how many students are taking algebra or biology. c. yes, because the sets, represented by the class taken, are disjoint, the cardinality of the union of the two sets is just the sum of the cardinality of each set. d. yes, because the intersection of the sets, represented by the class taken, is the sum of both sets.

Explanation:

The number of students taking algebra and the number taking biology are given. If there is an overlap (students taking both), the number of students taking either algebra or biology is less than the sum of the two individual - sized groups. Sets are disjoint if no element is common to both. Here, the sets of students taking algebra and biology are not necessarily disjoint.

Answer:

A. No, because the sets, represented by the class taken, are not necessarily disjoint. Some students may be taking algebra and biology.