(2) Suppose A is the set of students currently registered at the University of Calgary, B is the set of professors 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. Explain your answers.
(a) {(a, b) | a is taking a course from b} - This is not a function unless each student at the University of Calgary has just one professor, for if student a is taking courses from professor b1 and b2, the given set contains (a, b1) and (a, b2).
(b) {(a, c) | a’s first class each week is in c} – Yes, but explain why, please
(c) {(a, c) | a has a class in c on Friday afternoon}
I don't understand this at all, can someone put it in (a, c), (a, c) form.
A do not now
To determine whether each of the given sets is a function, we need to analyze if each element in the domain (set A) is associated with exactly one element in the codomain (set B or C).
(a) {(a, b) | a is taking a course from b}
This set is not a function unless each student at the University of Calgary has just one professor. If student 'a' is taking courses from professor 'b1' and 'b2', the given set contains (a, b1) and (a, b2), which means student 'a' is associated with two professors.
(b) {(a, c) | a's first class each week is in c}
This set is indeed a function because it represents a one-to-one relationship. Each student 'a' is associated with exactly one class 'c' that happens to be their first class each week. For example, if student 'a1' has their first class in 'c1' and student 'a2' has their first class in 'c2', the set would contain (a1, c1) and (a2, c2).
(c) {(a, c) | a has a class in c on Friday afternoon}
To represent this set in the (a, c) form, we can rewrite it as {(a, c) | a has a class on Friday afternoon, and c is the class}. This set is also a function since each student 'a' is associated with exactly one class 'c' that takes place on Friday afternoon. For example, if student 'a1' has a class 'c1' on Friday afternoon and student 'a2' has a class 'c2' on Friday afternoon, the set would contain (a1, c1) and (a2, c2).