Of the 12 full-time mathematics faculty at a high school, five drink coffee and eight do not enjoy teaching 8 a.m. classes. How many faculty both drink coffee AND enjoy teaching at 8 a.m.
Use Venn digagrams
Intersect two circles, label one C the other T
let the intersection be x
then the part of C outside the intersection is 5-x
the part of T outside the intersection is 8-x
5-x + x + 8-x = 12
x = 1
i don't kno
To find out how many faculty both drink coffee AND enjoy teaching at 8 a.m., we need to use the concepts of sets and intersection.
Let's represent the set of faculty who drink coffee as set A, and the set of faculty who enjoy teaching 8 a.m. classes as set B.
Given that there are 12 full-time mathematics faculty in total, we can conclude that the total number of faculty is the union of sets A and B, denoted as A ∪ B.
We are given that five faculty members drink coffee, which means the cardinality (number of elements) of set A is 5.
We are also given that eight faculty members do not enjoy teaching 8 a.m. classes, so the cardinality of the complement of set B, denoted as B', is 8. The complement of set B represents faculty who do not enjoy teaching 8 a.m. classes.
To find the number of faculty who both drink coffee (set A) and enjoy teaching at 8 a.m. (set B), we calculate the cardinality of the intersection of sets A and B, denoted as A ∩ B.
Using the formula for calculating the cardinality of the intersection of two sets, we have:
|A ∩ B| = |A| + |B| - |A ∪ B|
Substituting the given values:
|A ∩ B| = 5 + 8 - 12
Simplifying the equation:
|A ∩ B| = 13 - 12
|A ∩ B| = 1
Therefore, one faculty member both drinks coffee and enjoys teaching at 8 a.m.