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Discrete Math

Subgroup proofs

Let G be a group, not necessarily finite, and let H be subgroup G. (a) Prove that U = intersection of all x in G xHx^-1 is the largest normal subgroup of G contained in H. (b) Show that no proper subgroup H of A_5 contains six distinct Sylow 5-subgroups. I need a detailed rigorous proof of this to study please.

Providing subgroup proof

If |G|=p^n, where p is a prime, show that G has subgroups G_0, G_1, . . ., G_n with 1= G_0 <= G_1 <= . . . <= G_n =G such that [G_i : G_{i-1}] = p, 1 <= i <= n. I need a rigorous, detailed proof of this to study please.

Subgroup proof

Let A and B be finite subgroups of G. Even though AB need not be a subgroup of G, show that |AB||A n B| = |A||B|. (Hint: Define (a_1,b_1)~(a_2,b_2) iff a_1b_1 = a_2b_2. Prove that ~ is an equivalence relation and examine the equivalence classes.) I need a detailed and rigorous proof to study for a test p

Convergence proof.

Show that {a sub n} infinity. Converges to A iff n=1 {a sub n - A}infinity. Converges to 0 n=1. .

Closed set proof

A set F is closed iff for all x_n in F for all n in the naturals (x_n) converges to l, then l is in F. (x_n) is a sequence

Venn Diagram of Students' Dessert Preferences

Survey of 36 students Students' Preference: 25 Cake 20 Ice Cream 15 pie 2 all three 1 no desserts 15 cake or ice cream 8 pie or cake 3 ice cream only Draw a Venn Diagram that will represent the responses.

Sets, Subsets and Venn Diagrams

1. (3 points) - If A &#61645; B and B &#61645; C, can you conclude that A &#61645; C? Can you conclude that A &#61644; C? Definitions of symbols: &#8834; "is a proper subset of" &#8838; "is a subset of" &#8836; "is not a subset of" 1) Yes. All of the elements in A are in B, and all of the elements in B are in

Math help ... (Please see the attached file)

Hi, I need help with this assignment. I will be using this to check my work, so it very important that all work is shown so that I have a clear idea of how each problem is done. I am only interested in the completed assignment- not just some of it. Thank you very much for your help! :) (Please see the attached file) Instruct

Proof regarding direct sum of 2 copies of (Q,+)

Use the fact that any finitely generated subgroup of (Q,+), (the rationals under addition), is cyclic to show that (Q,+)+(Q,+), (the direct sum of two copies of (Q,+)), is not isomorphic to (Q,+). The first part of this was showing that any finitely generated subgroup of (Q,+) is cyclic and I understand that part and really had

Mathematics - Finite Mathematics Problem

Two movie theaters, UAI and UAII, start their movies at 7:00 p.m. The movie at UAI takes 75 minutes and the movie at UAII takes 90 minutes. If the shows run continuously, when will they again start at the same time?

Annuities

Retirement Annuity - When she is 30, Sue starts making annual deposits of $2,000 into a bondfund that pays 8% annual interest compounded continuously. Assuming that her deposits are made as a contiuous income flow, how much money will be in her account if she retires at age 55?

Mathematics - Finite Mathematics - Puzzle with Numbers

Solve this problem two different ways: Mensa is an association for people with high IQs. An advertisement for the organization offers the following challenge: "Take the instant test to see if you are a genius." PUT THE APPROPRIATE PLUS OR MINUS SIGNS BETWEEN THE NUMBERS, IN THE CORRECT PLACES, SO THAT THE SUM TOTAL WIL

Mathematics - Finite Mathematics on Quadratic Functions

1. Determine without graphing whether the given quadratic function has minimum value or maximum value. Then find the coordinates ... 2. Solve the Triangle. Round lengths ... 3. Solve the problem: One number is 6 less than a second number. Twice the second number is ... 4. Find the standard form of the equation of the el

Mathematics - Finite Mathematics..

In the textile industry, filament and yarn sizes are reported in denier which is defined as the mass in grams of a length of 9000 meters. If a synthetic fiber has an average specific gravity of 1.32 and a filament of this material has a denier of 5.0, what is the mass per unit length in pounds-mass per yard? What is the cross se

Mathematics - Finite Mathematics - Mensuration

Calculate the ratio of the area to the volume for a unit cube, a unit sphere inscribed inside the cube, and a right cylinder inscribed inside the cube. Next, for each having a unit volume (i.e., all three solids have the same volume) calculate the area-to-volume ratios for a sphere, cube, and cylinder.

Mathematics - Finite Mathematics - Base-3 System

Suppose that we wished to develop a base three number system to be used in place of either a decimal system or a base two binary system a-- How many separate symbols would we need in this system? In the binary system, we can get away with only two, 0 and 1. Will this work in a base three system? How would you write the decim

Mathematics - Finite Mathematics for Miles in a Lap

Question 1.The world record for the men's long jump is 29 3/8 feet. The women's record for the same event is 24 33/48 feet. How many feet longer is the men's record? Question 2. Each lap of the Indianapolis 500, a 500-mile car race, constitutes 1/200 of the race. How many miles are in a lap? Question 3. In a survey of fav

Euclidean metric proof

Let d be the usual Euclidean metric on R^n and f:R^n -> R^n be any function satisfying d(f(x),f(y))<d(x,y) for all distinct x,y in R^n. If B is a bounded subset of R^n such that f(B) is contained in B, show there is a unique b in the closure of B such that f(b) = b. I can show the uniqueness of such a b. Please give a detailed s

Comparisons to Complete Given Tasks

A. You are given a list of n names (all of the names are distinct) with instructions to put them in alphabetical order. How many comparisons are necessary to accomplish your task? B. After you have accomplished the task to part a, you are given another name. How many comparisons are necessary to place this name in its place i

Discrete Math

Let M be a two by two matrix for which each element is a real number, and let S be the set of all such matrices. Consider the mapping f of S to the real numbers R defined by the relation f(M) = determinant of M. a. Is this mapping onto? Why or why not? b. Is this mapping one to one? Why or why not? c. Is this mapping a h

Work and Time Problems

When three pumps, A, B, and C run together, they pump 3700 gallons/hour. When only A and B are running, 2700 gals/hr is the result and when only A and C are running, 2400 gals/hr is the result. What is the pumping capacity of the C pump, in gals/hr?

Mathematics - Solving a Finite Mathematics Problem

I am trying to work these problems not quite sure of how to work them. Find the equation of the line shown ... A bank loaned $15,000, some at an annual rate of 16% and some at an annual rate of 10%. If the income from these loans was $1800, how much was loaned at 10%? Write the augmented matrix of the system ... 2x

Exponential Functions ...

The expected future of Achworth, which presently has 2000 residents, can be approximated by the formula y=2000(e).02t , where t is the number of years in the future. A) Find the expected population of the town in years? B) How many years until the town will have doubled its population?

Numerical Analysis Problem Using Matlab

With the definition that pi is the area of the unit circle, explain why pi equals 8 times the integral from 0 to 1/sqrt(2) of (sqrt(1 - x^2) - x) dx. use the Romberg algorithm to approximate the integral. Provide the codes used and all the results and work.

Finite Mathematics - Number System - Amicable Pair

In 1866, a sixteen-year-old Italian student, Nicolo Paganini, discovered the second smallest amicable pair: 1184 = 2^5 x 11^2. Confirm that this pair is indeed amicable, but is not found by Thabit's rule. The second smallest amicable pair is (1184, 1210).

Finite Math - Fibonacci Umbers - Sum of Consecutive Integers

Fibonacci proved that if the sum of two consecutive integers is a square (that is, if n + (n - 1) = u^2 for some u), then the square of the larger integer will equal the sum of two nonzero squares. Verify this result and furnish several numerical examples.

Outs in Baseball Games

Please see attachment How many outs are there in a baseball game that lasts nine innings?....