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Discrete Math

Game Theory : Two-person, Constant-Sum Games

The attached file has a problem that I can't figure out how to set up. Can you take a look and explain how this problem should be set up? There are two people playing a two-person constant-sum game. Player 1 wants to travel from New York to Dallas using the shortest of the possible routes listed below. Player 2 has the ab

Chain breaking puzzle.

A traveler owing a gold chain with 7 links is accepted at an inn on condition that he pay one link of the chain for each day he stays. if the traveler is to pay daily and may be given links already used in payment as change, show that he only needs to take out one of the links of the chain in order to pay each day for 7 days. (n

Proof Set is Countable : Bolzano-Weierstrass Theorem

Given S is a subset of R Suppose S' (set of all accumulation points in S) = emptyset Prove S is countable. I think I am supposed to use the Bolzano-Weierstrass Theorem but I can't figure out how to apply it.

Revenue Function, Profit Function and Maximum Profit

Problem: A company makes cameras. The price per camera at which x million cameras can be sold is: p(x) = 94.8 - 5x. 0 -< x -< 15 (the symbol -< is the "greater or equal to sign", I couldn't get it to work on my computer) The cost of making x million cameras is: c(x) = 156 + 19.7x (x is in millions of

Proof : Prime Triplets

Show that there are no "prime triplets", that is numbers p, p+2, p+4, that are primes other than 3,5,7.

Symbolic Logic Problem : Proof

Construct a formal proof which shows that the sentence below is a theorem of predicate logic. *the E's are existential quantifiers (usually designated by backwards E's). the & are "and". Do not use quantifier negation rules. [(x)(~Rx or Nx)& ~(Ex)Nx or (Ey)(z)Szy] ->(~(Ex)Rx or (z)(Ey)Szy

Symbolic Logic Problem : Sentence to Expression

Transcribe the English argument below into an appropriate logical language adequate to determine it to be valid. Also, please provide a derivation of the conclusion from the premises within the same logical system (by which you transcribed it). *this seems to be predicate logic and probably requires universal and existential q

Symbolic Logic : Predicate Logic

The sentence below is a theorem of predicate logic. Show that it is by deriving it from the null set of premises. If any "individual" in the domain has a property, then every individual has it. I need help explaining this and with the derivation. (EX)(FX --->(Y)FY)

Symbolic Logic : Predicate Logic

The asterisk implies a conditional usually indicated by an arrow. The & sign indicates "and". In Aristotelian logic (X)(FX*GX) logically implies (EX)(FX & GX). Is this true in predicate logic? If not, why not?

Symbolic Logic Problem

I need to know how to construct a formal proof which shows that the sentence below is a theorem of predicate logic. The ^ sign indicates the word "or". The asterics indicates a conditional usually indicated by an arrow. No quantifier negation rules can be used. [(X)(~RX^NX)&~(EX)NX^(EY)(Z)SZY] * (~(EX)RX ^ (Z)(EY)SZY)

Symbolic Logic Problem

I have to determine whether or not this formal argument below is valid. If it is I have to provide a derivation of the conclusion from the premises, which I don't know how to do. If it is invalid, an interpretation which shows the invalidity must be constructed. The & signs mean "and" usually signified by a dot. The asterisk

Discrete Math : Probability, Functional Relations, Partitions and Primary Keys

Please see the attached file for the fully formatted problems. Name ________________________________ SSN __________________ CMSC 203 - Homework Assignment 4 - Due December 9, 2003 1. (a) Suppose I have a cooler full of cans of Coke, Pepsi, Sprite, Mountain Dew, Dr. Pepper, and Slice sodas. How many distinct ways can I li

Discrete Math: Logic

Please see the attached file for the fully formatted problems. Discrete Math True or False questions 1. Circle T if the corresponding statement is True or F if it is False. T F The Fibonacci Sequence is {sn | sn = sn&#61485;1 + sn&#61485;2, with s0 = 1 and s1 = 1}. T F The First (Weak) and Second (Strong) Principles of M

Discrete Math: Logic Problems, Truth Table and Rules of Inference

Please see the attached file for the fully formatted problems. 1. Construct the truth table for the compound proposition: [p &#61658;&#61472;(&#61656;q &#61614;&#61472;&#61656;r)] &#61611;&#61472;(&#61656;r &#61614;&#61472;&#61656;p) p q r ------------------------------------------------------------- T T T T T F T F T T

Prove Connectedness

Prove that G with at least (n-1)(n-2)/2+1 edges is connected, where n is the order of G.

Discrete math

SECTION 10.5 16. Consider the “divides” relation on the following set A. Draw the Hasse diagram for the relation. (See Overview for drawing tips.) b. A = {2, 3, 4, 6, 8, 9, 12, 18} 23. Find all greatest, least, maximal, and minimal elements for the relation in #16b. 42. Use the algorithm given in the text to find a

Discrete Math: Binary Relations

Please see the attached file for the fully formatted problems. SECTION 10.2 For #2: A binary relation is defined on the set A = {0, 1, 2, 3}. For the relation given, a. draw the directed graph (See drawing tips in the Overview) b. determine whether the relation is reflexive c. determine whether the relation is symmetr

Discrete Math: Binary Relations

Please see the attached file for the fully formatted problems. 2. Let C = {2, 3, 4, 5} and D = {3, 4} and define a binary relation S from C to D as follows: for all (x, y) for all (x, y) &#61646; C &#61620; D, (x, y) &#61646; S &#61659; x &#61619; y (Yes/No answers sufficient; explanation optional) a. Is 2 S

Discrete Math

Discrete math questions. Please provide formulas and all calculations for all 22. They are very short answer type questions.

Working with set theory.

Let A, B, and C be sets satisfying: A is included in B, B is included in C, and C is included in A. Prove that A = B = C.

Cutting a Cake-Game Theory Problem dealing with personal choices

Problem dealing with cutting a cake and personal choices Problem 2 There is a cake that is half lemon and half coffee. Steve values a whole lemon cake at $6, and a whole coffee cake at $10. Kevin values a whole lemon cake at $6 and a whole coffee cake at $4. Professor Raiffa suggests that they should divide the cake by

Game Theory Problem dealing with personal choices

Problem 1 1. Suppose you and one of your two roommates have just finished cleaning your dorm suite and found 13 quarters which you put on a table in the middle of the room. The third roommate who did none of the cleaning comes in from an afternoon of fun and relaxation and proposes that you divide the coins up the fol