Of the following sets, which represents a function?

A. (student's name, all the colors that the student likes)
B. (student's name, the student's favorite math teacher)

A. Only A
B. Only B
C. Both A and B
D. Neither A nor B



Answer :

To determine which of the given situations represents a function, we need to recall the definition of a function in mathematics. A function is a relation in which each element of the domain (input) is associated with exactly one element of the codomain (output).

Let's analyze each situation:

Situation A: (Student's name, all the colors that the student likes)

- Here, a student’s name (domain) is associated with all the colors that the student likes (codomain).
- Since a student can like multiple colors, a single student’s name can be associated with multiple colors.

Based on the definition of a function, Situation A does not represent a function because there isn't a one-to-one association; a single element in the domain can be mapped to multiple elements in the codomain.

Situation B: (Student's name, the student's favorite math teacher)

- In this situation, a student’s name (domain) is associated with the student’s favorite math teacher (codomain).
- Each student can only have one favorite math teacher at any given time.

Given the definition of a function, Situation B does represent a function since each student’s name is associated with exactly one favorite math teacher, thus ensuring a one-to-one association.

Therefore, based on this analysis:

- Only A is not correct because Situation A does not satisfy the criteria for a function.
- Only B is correct because Situation B does satisfy the criteria for a function.
- Both A and B is not correct because only Situation B is a function.
- Neither A nor B is not correct because Situation B is a function.

Thus, the correct answer is:

Only B