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    Discrete Math

    Venn Diagram Graduate Applications

    A company has 40 applicants for a particular position. 30 of the applicants are male. 35 of the applicants are college graduates. 27 of the male applicants are college graduates. a. With this information, I need to create a Venn Diagram that describes this situation. b. How many male applicants are not college graduates?

    Singleton bound, sphere-packing bound and Varshamor-Gilbert

    Can you explain what do Singleton bound, the sphere-packing bound and the Varshamor-Gilbert mean? Determine what the Singleton bound, the sphere-packing bound and the Varshamor-Gilbert bound say about the maximum number of information bits that codewords with ten check bits can have if the codewords are protected from 3 or f

    Proof question of group

    Prove or disprove the following: Let G be a group, f, g . G, and fg gf , then | <f, g> | > 5. See attached file for full problem description.

    Truth Values : Predicates and Quantifiers

    Determine the truth value of the statement $x"y(x<= y²) (and explain your answer) if the universe of discourse for the variables consists of: a) the positive real numbers b) the integers c) the nonzero real numbers

    Solve: Sets and Venn Diagrams

    Please view the attachment to see questions 1 and 2. 3. A survey of 10355 people restricted to those who were either female or Hispanic or over 16 years of age, produced the following data: Female: 6022 Hispanic female: 2136 Hispanic: 3564 Over 16 and female: 959 Over 16: 4722 Over 16 and Hispanic: 1341 His

    St. Petersburg Paradox

    A person tosses a fair coin until a tail appears for the first time. If the tail appears on the nth flip, the person wins 2n dollars. Before the nth flip, he does not receive nor pay anything. Let X denote the player's winnings. Show that E(X)=&#61537;&#61486;&#61472;Would you be willing to pay $1 million to play this game? Woul

    Proofs : GCDs and Primes

    1. (i) Find the gcd (210, 48) using factorizations into primes (ii)Find (1234, 5678) 2. Prove that there are no integers x, y, and z such that x^2 + y^2 + z^2 = 999 keywords: greatest comon divisor

    Linear Combinations, Division and the Euclidean Algorithm

    Assume that d=sa+tb is a linear combination of integers a and b. Find infinitely many pairs of integers ( s sub k, t sub k ) with d=s sub k a + t sub k b Hint: If 2s +3t =1, then 2 (s+3) + 3 (t-2) = 1 I would like a very detailed, as possible, exp

    Logical reasoning problem with multiple variables

    It was unfortunate that Rose and the other four coworkers in her department live in different suburbs because otherwise they might have been able to carpool. As it stands, each of the five drives to work every day on a different route. Every day last week from Monday through Friday, one of the five arrived late to work because o

    Equivalence Relations and Classes

    For m, n, in N define m~n if m^2 ? n^2 is a multiple of 3. (a.) Show that ~ is an equivalence relation on N. (b.) List four elements in the equivalence class [0]. c) List four elements in the equivalence class [1]. (d.) Are there any more equivalence classes. Explain your answer.

    Mod and Divisibility Proof

    Let i, j, n be positive integers with i > j. Let f(x) in Zn[x] have non-zero constant term, and let d = o(x mod f(x)). Suppose that x^i and x^j have the same remainder on division by f(x). Prove that i-j >= d. -- Theorem 4.7.2 Suppose that F is a field of order |F| = q and that f(x) in F[x] has degree n >= 1 and has non-zer

    Proof: Intergers Modulo n

    Prove that if a-bar,b-bar є (Z/nZ)^x then a-bar.b-bar є (Z/nZ)^x Please see the attached file for the fully formatted problems.

    Construction and Proof Involving Line Segments

    Given a line segment QR=1 1. Given segments q and r, construct a line segment qr. 2. Given segments q, r, s construct a line segment qrs. I'm confused on how to set it up and begin. I have the one for constructing a line segment of length q/r. Thanks

    Drawing Venn Diagrams

    Make a venn diagram: 25 students play soccer, 4 boys play soccer and baseball, 3 girls play soccer and baseball, 10 boys play baseball, 4 girls play baseball, 3 boys plays baseball and tennis, 1 girl plays baseball and tennis, 1 boy plays all three sports, 1 girl plays all three sports, 9 students play tennis, 3 boys play soccer

    Game Theory : Two Person Zero Sum Game

    Two armies are advancing on two cities. The first army has 4 regiments and the second army has 3 regiments. At each city, the army that send more regiments to the city captures both the city and the opposing army regiment. If both armies send the same number of regiments to a city, them the battle at the city is a draw. Each

    Two-Person Zero-Sum Game Problem

    Need help setting up this 3X4 Matrix problem. I have only worked 2X2 matrix game problems per recent homework, however, I can't seem to leverage that knowledge for this problem. I'm also not sure how to deal with the extra reward variable (one point for capturing each of the other army's bn). Also need help setting up the LP for

    Continuity

    Show that any function from a discrete metric space X into a metric space Y is continuous.

    Applications of Functions Word Problems

    1. Solve the equation. 3(6 - 3x) = 1/27 2. Use natural logarithms to evaluate the logarithm to the nearest hundredth. log√4 ^259.5 3. Solve the problem. Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at $45000 with a raise each March 1 of 3 % Chris starts at $33000 with a raise on Mar

    Continuity Proof Intervals

    Assume that f(x) is continuous in some open interval J that contains the point a, f'(x) exists for each x and limit of f'(x) as x&#61664;a exists. Prove that f is differentiable at a and f'(a)=limit of f'(x) as x&#61664;a keywords: differentiability

    Algorithm Implementation of Edge Triggered

    (See attached file for full problem description) 1. S-R Latch Given the following NAND implementation of an S-R latch, Write its truth table. Qt St Rt Qt+1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 2. Gate S-R latch. Given the following implementation of a gated (clocked) S-R latch and its t

    Euler's theorem applied to large integers

    Consider Euler's theorem: If m is a positive integer and a is an integer relatively prime to m, then a^phi(m)&#8801;1(mod m) Use this theorem to show that if a is an integer relatively prime to 32760 then a^12&#8801;1(mod 32760). Symbols better shown in file (attached).

    Operations Research

    Infocomp Systems is a research and development laboratory firm that develops computer systems and software primarily for the medical industry. The laboratory has proposals from its own researchers for eight new projects. Each of the proposed research projects requires limited resources and it is not possible to undertake all

    Matlab plot of the spectrum of the signal

    Create a simple low-pass filter consisting of 10 1's in a row lpf = ones(1,10) Plot the spectrum of the signal using the command: plot(abs(fft([lpf zeros(1,246)]))); Indicate the frequency of the first zero in the frequency response in terms of the sampling frequency (frequency(bin#) = (bin#-1)*fs/(N_bins)