Suppose A is the set of students registered at the University of Calgary, and C is the set of courses currently being offered at the University of Calgary. Under what conditions is each of the following a function?

a)
{(a, c) | a’s first class each week is in c}
b)
{(a, c) | a has a class in c Saturday evening}

What do you think?

not sure confused

To determine whether each of the given cases is a function, we need to ensure that each element in the first set maps to exactly one element in the second set.

a) {(a, c) | a’s first class each week is in c}

In this case, the first set consists of students in set A, and the second set consists of courses in set C. For each student in A, we need to determine if their first class each week is uniquely mapped to a particular course in C.

To check if it is a function, we need to examine each student in A and ensure that their first class each week is indeed in a single course in C.

b) {(a, c) | a has a class in c Saturday evening}

In this case, the first set also consists of students in set A, and the second set consists of courses in set C. Now, for each student in A, we need to determine if they have a class specifically on Saturday evening, and whether this class is uniquely mapped to a course in C.

To check if it is a function, we need to examine each student in A and determine if they have a class specifically on Saturday evening, and if this class is indeed in a single course in C.

In both cases, to determine if a student's class is in a particular course, we need more specific information about the University of Calgary, its courses, and class schedules. Without this information, we cannot accurately determine whether these sets are functions.

Therefore, in order to determine if each case is a function, we need additional information from the University of Calgary regarding class schedules and how classes are assigned to courses.