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
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a) If there are no two students with a common phone, the function that assigns to a student his or her mobile phone number is on-to-one.
b) Since the student identification number is unique, and hence there are no two students with the same identification number, the function that assigns to a student his or her identification number number is on-to-one.
c) Two student can have the same final grade in the class. Therefore, in general case this function is not one-to-one. It can be one-to-one if the number of students is less or equal to the number of final grades and different students have different final grades.
d) This function in general case is not one-to-one because of two students can live in the same town. It can be injective if different students have different home town.