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# Discrete Math

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?

### Need to apply the Shere-Paking bound and Varshanov-Gilbert bound to know this code is linear.

Determine whether there can exist a linear binary code with the parameters [n,k,d]=[12,7,5] In here we need to apply the Shere-paking bound and Varshanov-gilbert bound to know this code is linear. I think when this code satisfies the shere-packing we do not it is a code when satisfies we know it is not a code and when it

### 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

### A question of group action

See attached file for full problem description.

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

### Complete Graphs and Cycles; Undirected & Spanning Trees and Reverse Polish Notation

Consider a comple graph G, n &#8805; 3. Find the number of cycles in G of length n. How many cycles in a complete graph with 5 vertices? Another problem is attached involving Reverse Polish Notation.... Please see the attached file for the fully formatted problems.

### 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

### Collection of subsets for equivalence relations

Let S be a collection of subsets of X, X = US. [S is not necessarily peicewise disjoint.] xRy if x, y &#1028; S &#8834; S. Is R necessarily an equivalence relation? Show why or why not.

### 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.

### Proof : Equivalence Relations and Divisibility

Prove 8|5^(n+1) +(2)3^n + 1, n Є N

### 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 : For every positive integer n, prove that 1+2+...+n=n(n+1)/2.

Problem: For every positive integer n, prove that 1+2+...+n=n(n+1)/2.

### 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

### Real Anaylsis : Metrics Proof

Let d be a metric in X. Prove that p(x,y)=(d(x,y))/(1+d(x,y)) is also a metric in X.

### 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)