. Consider the functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a student his or her a) mobile phone number. b) student identification number. c) final grade in the class. d) home town

a) The function from the set of discrete mathematics students in a class to their mobile numbers is a one-to-one function because any two of students cannot have a same mobile number. 

b) The function from the set of discrete mathematics students in a class to their identification numbers is a one-to-one function because every student has a unique identification number and each student has a single identification number. 

c) The function from the set of discrete mathematics students in a class to their final grades depends on the number of students and the number of grades. Most likely not a one-to-one if more than one student has the same grade. 

d) The function from the set of discrete mathematics students in a class to their hometown depends on the number of students and the number of towns. Most likely not a one-to-one if more than one student belongs to the same town. 

If the number of students is less than or equal to the number of towns and each student belongs to a different town then the function is one-to-one.