Jane Doe was involved in the sale of used tractors and trucks and owned a dealership in Seymour, Texas named Owl Farming Motors. Doe regularly engaged in the practice of rolling back the vehicle odometers when her employees were off duty. Doe would then go back and modify the paperwork to reflect the modified usage and then sell the tractors and trucks for higher prices based on their status as "low mileage" used vehicles. Several customers expressed to the salespeople that they were surprised to find used vehicles with such low usage for sale in the area and that the low mileage was a key reason for their decision to buy at OwI Farming Motors. Eventually, customers discover that the vehicles they purchased were altered and complain to the police who then conduct an investigation and determine that there is probable cause that Doe committed a crime. They then prepare an affidavit setting forth the basis for the case against Doe and appear before a judge to obtain a valid warrant for Doe's arrest. After Doe is arrested, she freely tells the arresting officers that she modified the odometers on the way to the station without them even asking her a question about it$.$ At the station she is then Mirandized for the first time by a detective and then refuses to answer any further questions and asks for a lawyer. $1.$ What is a crime? Under these facts, has a crime actually been committed? If so$,$ what crime $($please limit your answer to the crimes identified in the text$)$ has been committed? $2.$ What is meant by elements of a crime and what are the specific elements of the crime$($s$)$ that you identified for this situation? $3.$ Do you agree with the investigator that a probable cause exists that a crime was committed by Doe? Meaning, are all of the elements of the crime$($s$)$ identified by you established by these facts? $($Please explain your answer.$)4.$ Will Doe's statements admitting to her actions to the arresting officers be admissible during her trial? Why or why not?