A college survey was taken to determine where students study. Of 118 students surveyed , 70 studied in the library , 57 studied in the student union , 21 studied in both the library and the student union .
To solve this problem, we can use the principle of inclusion-exclusion. First, we know that the number of students who studied in either the library or the student union is:
70 + 57 = 127.
However, this counts the 21 students who studied in both the library and the student union twice. So we need to subtract this number from the total:
127 - 21 = 106.
Therefore, there are 106 students who studied in either the library or the student union, but not both.
To determine the number of students who studied exclusively in the library, we need to subtract the number of students who studied in both the library and the student union from the total number of students who studied in the library.
Total students who studied in the library = 70
Students who studied in both the library and the student union = 21
Number of students who exclusively studied in the library = Total students who studied in the library - Students who studied in both the library and student union
= 70 - 21
= 49
Therefore, 49 students studied exclusively in the library.
To determine the number of students who studied in either the library or the student union, we can use the formula for finding the union of two sets:
Union(A, B) = |A| + |B| - Intersection(A, B)
Given that 70 students studied in the library (A), 57 students studied in the student union (B), and 21 students studied in both the library and the student union (Intersection(A, B)), we can calculate the number of students who studied in either location:
Union(A, B) = 70 + 57 - 21
= 127
Therefore, 127 students studied in either the library or the student union.