### Binary Operations : Idempotence

An element e of a monoid M is called an idempotent if e^2 = e. If M is finite, show that some positive power of every element is an idempotent.

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An element e of a monoid M is called an idempotent if e^2 = e. If M is finite, show that some positive power of every element is an idempotent.

Consider the Cayley table: (see file) Show that there is only one way to complete table (1) so that the resulting operation is associative, and that the result makes {a,b} into a commutative monoid.

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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

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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

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1 + sn2, with s0 = 1 and s1 = 1}. T F The First (Weak) and Second (Strong) Principles of M

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Please response to the following: Reason each step and explain the mathematical mistake if there is one. (a+b)(a-b) = b(a-b)

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

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

Find gcd (435, 377), and express it as a linear combination of 435 and 377..

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.

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

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

Prove whether the following is true or false. If it is false give a counter example. If M is a connected point set, the cl(M) is connected.

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A function f(x) is defined on a set of real numbers x not equal to 0 as: f(x) = (2x +1)/x. Is f(x) one to one?