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Prove that 3n<n! if n is an integer greater than 6.

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 20E Chapter 5.1

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 20E

Problem 20E

Prove that 3n<n! if n is an integer greater than 6.

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2/23/16 CHAPTER 8 – Intellectual Property Rights Important things – trademarks, patents, copyrights, trade dress, and trade secrets  Intellectual property – a property that results from the intellectual and creative process of a person, company, or business  Although ideas are intangible, they are some of the most important assets if companies and therefore need to be protected  Trademark – a distinctive work, symbol, sound, or design that identifies the manufacturer as the source of particular goods and distinguishes its products from those made or sold by others o By using another’s trademark, a business could lead consumers to believe that its goods were made by the other company o Protection for a symbol 2/25/16  Trade dress – refers to the image and appearance of a product o Protected to the same degree as a trademark  Trade secrets – anything that makes an individual company unique and would have value to a competitor o Ex. customer lists, marketing techniques, production methods  Patent – gives an inventor the exclusive right to make and sell a product for 20 years o Patents for designs are 14 years o The America invents act – the first person to file an application receives protection  Copyrights – a property right granted to the author/originator of certain literary or artistic productions o Protection is automatic o Infringement – occurs whenever the form or expression of an idea is copies o The reproduction does not have to be exactly the same as the original 3/01/16 CHAPTER 10  Contract (K) – involves an offer, acceptance, and consideration for the breach of which the law provides a remedy important o Elements: must have all  Agreement: offer + acceptance  Consideration – something of value must be received or promised  Capacity – both parties must be competent to enter a contract  Legality – the contract’s purpose must be legal  Genuine consent (voluntary)  Form – some must be put in writing  Fair price is not an element o Bilateral – a promise for a promise o Unilateral – a promise for a fact o Formal – must be in a specified format to be enforceable o Informal – no special format is required o Express – formed by words o Implied – formed by the conduct of the parties o If the word ends in “or” the person made the contract o If the word ends in “ee” the person accepts the contract  Ex. Mortgagor is the person who needs the money, mortgagee is the person lending it o Contracts can be for services, real property (reality, real estate, land), or personal property 3/03/16  Agreement – requires an offer and acceptance o Offeror – the one who makes the offer (revoke) o Offeree – the one to whom the offer is made (reject) o Requirements – intention to create a contract, reasonably certain terms, communication o Option contract – hold the offer open for a specific period of time in exchange for consideration  Minors: can enter into contracts, but they are avoidable at the minor’s request (disaffirmance)  Contracts contrary to statute: o Contracts to commit a crime o Usury – charging an illegal interest rate IMPORTANT o Gambling o Incensing statutes  Contracts contrary to public policy: o Contracts in restraint of trade o Unconscious contracts – enforcement would be unduly unfair o Exculpatory clauses 3/15/16  Form: o Under the statute of frauds, certain contracts must be in writing  Contracts involving land  Contracts that cannot be performed within one year and one ay of execution  Contracts to answer the debts of another  Promises in consideration of marriage  Contracts for the sale of goods $500 or more  Marriage, Year, Land, Executor contracts (guaranty), Goods over $500 – MYLEG o Exceptions: Confirmations, Admissions, Part performance (started to perform contract), Promissory Estoppel – detrimental reliance, Specially made goods (CAPPS) 3/17/16 CHAPTER 11 – Contract Performance, Breach, and Remedies  Voluntary consent – lack of consent can be a defense to enforceability – contracts can be voided if there was no consent  Mistakes of fact: o Bilateral – either party can rescind the contract o Unilateral – a mistake regarding a material fact, the person must have known or should have known about the error  Fraudulent Misrepresentation – a misrepresentation of material fact occurred o An intent to deceive o The innocent party justifiably relied on misrepresentation o The party was harmed as a result of the misrepresentation  Parties can transfer contract rights to a third party: o Delegation – transferring duties to another o Assignment – transferring rights to another  Assignments: o Assignor – assigns the rights o Assignee – receives the rights o The assignee can demand performance from the original contracting party o All rights can be assigned unless:  The assignment is prohibited by statute  The contract is personal  It significantly changes the risk or duties of the obligation  The contract prohibits assignment  Delegations: o Parties:  Delegator – delegates the duties  Delegatee – receives the delegation  If the delegate doesn’t perform, the delegator is obligated to do so  Third Party Rights: o Beneficiaries: when the original parties contract to benefit a third person, that person is an intended third party beneficiary o Intended beneficiary – has legal rights and can sue the promisor for breaching the contract  Discharge – the termination of the contract obligation o Occurs when the parties have fully performed their contractual obligations  Anticipatory repudiation – when one person asserts that they will not be fulfilling their end of the contract – this is treated as a material breach o The other party can immediately sue for damages  Types of damages: IMPORTANT o Compensatory – direct losses and costs o Consequential – indirect and foreseeable losses o Punitive – to punish and deter wrongdoing o Nominal – to recognize wrongdoing when no monetary loss is shown 3/22/16  Mitigation of damages – when a breach occurs, the non-breaching party has a duty to reduce damages  Liquidated damages – specific amount agreed to be paid as damages in the event of future breach  Penalty – designed to penalize, generally unenforceable CHAPTER 12 – The Uniform Commercial Code  Uniform commercial code (UCC) – a set of rules that a group of business scholars assembled which provides the rules involving goods/personal property o Allows parties to form contracts more easily than the common law o Applies to personal transactions  Applies to all states!!!  Article 2 – covers sales (of goods)  Article 2A – covers leases (of goods)  Merchant – a person/company that holds itself out by occupation by having knowledge or skill unique to the transaction o Can be a seller or buyer  Consumers – a person without strong knowledge/skill to the transaction o Can be a seller or buyer  The provision that cannot be left open in a contract – quantity  All contracts DO NOT have to be in writing to be enforceable under the UCC o Sales of goods under $500 do not have to be in writing

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Chapter 5.1, Problem 20E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Prove that 3n<n! if n is an integer greater than 6.