Problem 17E

Consider these functions from the set of teachers in a school. Under what conditions is the function one-to-one if it assigns to a teacher his or her

a) office.

b) assigned bus to chaperone in a group of buses taking students on a field trip.

c) salary.

d) social security number.

Solution:

Step1

Given that

A functions from the set of teachers in a school.

Step2

To find

We have to find conditions is the function one-to-one if it assigns to a teacher his or her?

Step3

One -to -One :- A function for which every element of the range of the function corresponds to exactly one element of the domain. We can write one-to-one as 1-1.

a. Office.

1. The function one-to-one if it assigns to a teacher his or her Office.

Condition:-It depends on whether they share their office or not.Possible that every teacher has single office.

2.The function not one-to-one if it assigns to a teacher his or her Office.

Condition:- If they share their office then two or more than two teachers have the same office.

Step4

b) assigned bus to chaperone in a group of buses taking students on a field trip.

1. The function one-to-one if it assigns to a teacher his or her assigned bus to chaperone in a group of buses taking students on a field trip.

Condition:-Just a single teacher is a chaperone for a bus and no two teacher are chaperone for same bus.

2.The function not one-to-one if it assigns to a teacher his or her assigned bus to chaperone in a group of buses taking students on a field trip.

Condition:- If two teacher are chaperone for same bus.

Step5

c) salary.

The function not one-to-one if it assigns to a teacher his or her salary.

Condition:-It depends on academic and administration.

Step6

d) social security number.

The function one-to-one if it assigns to a teacher his or her social security number.

Condition:- Because each teacher will have only one social security number and no two teacher have same.