. 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

Function f:X -> Y is called one-to-one if and only if $\forall a,b\in X:f(a)=f(b)\to a =b$

a) Y is the set of mobile phones. Since two different students cannot have identical mobile phone number, then f:X -> Y is one-to-one function

b) Y is the set of a students identification numbers. Since two different students cannot have identical student identification number, then f:X -> Y is one-to-one function

c) Y is the set of the possible final grades in the class. Since two different students can have identical final grades(it is posiible that more than one student will get, for example, b), the condition of an one-to-one function doesn't met, so f:X -> Y is not one-to-one function

d) Y is the set of towns. Since two different students can have identical home towns (it is posiible that more than one student will be, for example, from Denver), the condition of an one-to-one function doesn't met, so f:X -> Y is not one-to-one function