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a. Find an inverse for 210 modulo 13.b. Find a positive

Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp ISBN: 9780495391326 48

Solution for problem 31E Chapter 8.4

Discrete Mathematics with Applications | 4th Edition

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Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp

Discrete Mathematics with Applications | 4th Edition

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Problem 31E

Problem 31E

a. Find an inverse for 210 modulo 13.

b. Find a positive inverse for 210 modulo 13.

c. Find a positive solution for the congruence 210x ≡ 8 (mod 13).

Step-by-Step Solution:
Step 1 of 3

Chapter 12 I. Torts Definition Tort: (Common law jurisdictions) is a civil wrong that unfairly causes someone else to suffer loss or harm Resulting in legal liability for the person who commits the tortious act Types of torts Intentional On purpose Transferred intent: An intention to do a tort but not directly affecting the one the intent is placed on Negligence An accident Strict Liability Engaging in activities that are abnormally dangerous, anything that goes wrong makes one liable You mess up, you will pay Elements of Torts: Must have all to classify a tort Duty (∆) Legal duty of defendant, not ethical duty Often voluntary Not contract based (K) Example: CPR Certified If you injure the person while trying to perform CPR you can be sued. Breach of Duty Do not perform duty correctly Causation Factual: Did your actions lead up to the result; were you part of this Proximate: Fault, were you part of the scenario and do you have some liability Harm Injuries: Bodily injuries, sometimes death Can be mental injuries Damages: Assets, monetary value II. Intentional Torts The threat of a punch and the actual punch Assault: A threat of harmful or offensive touching in near future Does not have to be exclusively about one’s person, can be with one’s assets Other compenents One being immediately worried about offensive action. Talking about the punch or getting close with a punch Someone bringing a threat to another but is not actual executed. Battery: An act of harmful or offensive touching The impact of the punch Can sometimes be without Assault False Imprisonment: The intentional confinement of a person; feeling of being trapped can bring legal action Merchant protective stature: If someone is shoplifting, a merchant can hold the person in confinement for a reasonable period of time. Upheld in all 50 states Behavior and Speech Infliction of Emotional Distress: An act of “extreme and outrageous” behavior; proof is required Defamation: Harm to one’s reputation and good name Forms of Slander: Spoken defamation Libel: Written defamation Often with public figures Malice: Doing defamation with the intent to harm one’s reputation Invasion of Privacy Derive from common law Depends on setting of scene Fraud: When one lies about a contract of a purchase/service Getting ripped off Most common intentional tort Need material fact to bring legal action; something worthwhile Realty/Property Trespass: One is at a property they are not allowed access to Not often with harm, but connected with theft or vandalism makes a stronger case (π) Conversion: The act of taking one’s assets, steal it, and sell it Larceny: Conversion without threat Robbery: Conversion with threat Nuisance: One’s actions makes another person not possible to enjoy their property Example: Noise complaints Relationship & General Business torts Wrongful interference with a Contractual Relationship: A third party influencing a party to break contract Scenario: A -K-> B; C influences to break contract B sues A for breaching of contract B sues C for wrongful interference Only if C directly speaks with A can the legal action be brought up Wrongful interference with a Business Relationship: The direct solicitation of one’s company and interference of a rival’s business Scenario: Have employees sit out in rival’s store to market own store; direct contact Wrongful Entering into Business: Predatory tort with intentions/goal to destroy competition Evidence is selling at a loss Business Defamation Disparagement: Business defamation; Making false allegations of a business rival Slander of Quality (Trade Libel): Stating that a business’s products are not good/unsafe; Ingredients safety Title: Question of ownership; Example: Used car salesman says the cars are stolen Appropriation: Using someone’s work, ID, etc. Being the unknown spokesman Money Laundering: Moving money from illegal enterprises to investment capital If one deposits more than 10k in cash, the bank must alert the Federal Government Having a huge cash amount and trying to bring it towards banks Chapter 13 III. Negligence Tort elements: Reference Ch. 12 Definition: An accidental tort; without acting responsible causes liability Intervening/Supervening Force Intervening: Showing proximate cause only goes so far. A force that acts after another's negligent act or omission has occurred and that causes injury to another Supervening: A force that operates independently of anything else and becomes the proximate cause of an accident. Example: Getting in car accident, go to hospital, hospital screws up surgery. Hospital is now liable for further injuries Duty of Care Invitee/Customers: Keeping shop safe Licensee: Lesser duty for salesmen, delivery people; includes social guests Trespasser: Cannot purposefully endanger them Common sense and Negligence Negligence Per Se: Not living up to standard law & regulation in business Example: Speeding Res Ipsa Loquitur: "It speaks for itself" The assumption of negligence, someone is negligent or else the incident wouldn’t have occurred Proving one is not negligent Types of Negligence Judgement Contributory: If one is a major component of their own harm, you cannot bring an action Not a common practice in most states Example: On bicycle without reflectors and gets hurt, that person is major factor of the harm Comparative: Ratio analysis of negligence in both parties. More common practice in state law Example: Being 90% liability but still being able to sue Assumption of Risk Knowing something is wrong (a product) and assuming there is no risk in using said product Strict Liability Abnormally Dangerous Activity: To engage in said activity makes one liable for all actions High Risk Negligent Inflection of Emotional Distress: Doing something unintentional and causing distress to a bystander DANGER ZONE!!!!!: Amount of space between action necessary to bring legal action Note: Being outside of zone you can still be distressed but you cannot do legal action Chapter 11 IV. Business Fears Warranties: Promises of a business Implied: Court defined warranty Title With selling a product the seller transfers ownership to the buy Seller has authority to sell good Seller and buyer have responsibility with product Merchantability Seller is going to sell product with at least average quality Includes food Example: Blue Ship Tea Room and Fish bone in soup Fitness Using a seller’s expertise Express: Explicitly stated and voluntary; does not have to be given "If you don’t like it, you can get your money back.” Is not a forced warranty Magnuson-Moss Warranty Act: Guidelines of supplying a warranty Types of warranty Limited: Given time frame Full: Anything and everything is covered Dollar amounts and warranty Sub $20 Joke of a case, not worth covering Past $20 Can be significant, worth covering V. Product Liability Caveat Emptor vs. Caveat Venditor Emptor: Buyer Beware. If it breaks it’s because the customer bought the wrong problem Venditor: Let the seller beware, pro-consumer to a fault Comparative and Contributory Comparative Negligence One can cover from negligence that is not one’s fault Contributory Negligence If buyer is at biggest fault the seller cannot be sued Statute of Limitations v. Statute of Repose Limitations Limited period of time to bring legal action, is not a set in stone Normally 3-7 years Repose When can seller not worry about bad product any longer Being relax about product Answer: When the product stands the test of the market and is safe Normally 10-15 years Example: Long selling product that has not had chronic issues and is behind updated safety protocol Chain of products Part manufacture; defendant Wholesaler; defendant Retail; defendant Buyer: Can sue everyone in chain of product; plaintiff or defendant Types of second buyers 2nd hand purchases Lease Donations/Guest Injured bystander A second hand buyer can sue the first hand buyer Privity: Bringing action against those that have direct contact with defected product Not a common defense anymore Assumption of Risk: Knowing a product is no good but still using it Misuse of Product: Not properly using a product for seller’s purpose Crash Worthiness Doctrine: Crashing a car is a misuse of the product. The doctrine tells auto makers to make safer more durable vehicle. Chapter 7 VI. Criminal Law Felony v. Misdemeanor Felony: Potential more than a year or more in prison. Potential capital punishment. Misdemeanor: Potential less than a year or more in prison. ALL ABOUT POTENTIAL Actus Reus and Mens Rea Actus Reus: What did you do (ACT) Mens Rea: What are you thinking (MEN)TAL Felon, Murder Rule If one engages in a dangerous felony and any homicide occurs makes the case “murder 1" Allows for death penalty Co-conspirator counts Defenses Infancy: I am too young to understand what I did Will not learn from punishment If under 7 years of age, you cannot truly commit a crime Ages 7-14, probably too young but with enough pre-meditation can get jail Ages 14+, criminal law applies If felon is heinous enough, can be tried as an adult Intoxication: I am too drunk to understand what I did “Liquid courage” won’t be a good excuse. Voluntary intoxication: Consuming intoxicants until reaching mental states Involuntary intoxication: Hazing circumstances, switching medicines without knowledge Insanity: I am too crazy to understand what I did Not being able to hold self responsible from mental stage “Snapping”, irresistible impulses. Tough sell. Mental state limitations Treatment, asylum, etc. Consent: Agreeing to conduct actions (Self-defense) Example: Contact sports Mistake: Not knowing something is a crime Duress: “They made me” Being forced into doing an action Threat vs. Action Action is worse than threat Weak defense Action is as bad than threat Very weak defense Action is less than threat Good defense Justifiable use of force: To use a reasonable amount of force in defense, anything past is excessive Deadly Force: To protect yourself and others from potential death is justified. NOT THINGS Immunity: Cutting a deal and giving someone legal protection or lighter sentencing Often with co-conspirators to snitch on other conspirators Diplomatic immunity: Little to do with criminal law with embassies and/or diplomats Miranda Warnings: The notification of rights (at arrest) prior to interrogation Probable Cause: A higher-likelihood that you are guilty of actions that are against societal activities Applies to establishing need for search warrant White Collar Crime: Crime that business professionals are active in Embezzlement, insider trading, etc. Nonviolent crime. RICO Act: Racketeer (Mafia/Organized Crime) Influenced Corrupt Organizations Act Goal: Tries to keep organized crime money out of legit business What it actually does: Practically works for any fraud and money laundering Entrapment: For authorities to try and lure innocent people into doing a crime A sting operation against known criminals is legal Common Law Felonies Murder 1: Premeditated 2: Accidental Rape Sex crime Manslaughter Accidental or unintended injury Robbery Taking property with violence or threat of violence Sodomy Sex crime Larceny (Grand) Taking property without violence or threat of violence; stealthy Grand larceny: Taking something with good value Arson Purposeful burning of a another’s property Mayhem Purposeful disfigurement of a human being Burglary Breaking and entering, regardless of property and time of day. Intent to commit another felony. Breaking and entering is tampering with entrances Statutes Statutes of Limitations Similar to civil, time frame to bring in legal action Homicides do not have statute of limitations Rapes do not have statute of limitations

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Chapter 8.4, Problem 31E is Solved
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Textbook: Discrete Mathematics with Applications
Edition: 4
Author: Susanna S. Epp
ISBN: 9780495391326

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a. Find an inverse for 210 modulo 13.b. Find a positive