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Discrete Structures

Truth tables

Let p represent some false statement and let q represent some true statement. What is the truth value of each of the following: a. ~(~p v q) b. ~(p v q) c. (~p) v q

Multinomial experiment, Expected Frequency

1. True or False. In a multinomial experiment, all outcomes of each trial can have several categories. 2. In finding Expected Frequency you multiply what divided by what?

Discrete Structures : Congruences

Construct addition and multiplication tables for arithmetic modulo 11. For example, 7 + 8 mod 11 is 4 and 7*8 mod 11 is 1 so the entry in row 7, column 8 would be 4 for the addition table and 1 for the multiplication table. Use your tables to solve each of the following congruences: a. 3x+2≡8 (mod11) b. 3x-5≡2 (m

Discrete Structures : Reflexive, Symmetric or Transitive Relation

Let S ne the set of all strings of a's and b's. Let R be the relation on S defined by... x and y begin with different symbols. Determine, and prove your answers, whether or not R is reflexive, symmetric or transitive. Please see the attached file for the fully formatted problems.

Discrete Structures : Onto and One-to-one

Prove or disprove (find a counterexample) : If A C B and f : A --> B is an onto function (the range of f is all of B), then f is one-to-one and A =B. Please see the attached file for the fully formatted problem.

Set problem

If U = {a,b,c,d,e,f} A = {a,b} B = {-1, 0, 11} Find A' Find B' Find (A U B)' Find (A ∩ B)

Consider an experiment that consists of determining the type of job?either blue-collar or white-collar?and the political affiliation?Republican, Democratic, or Independent?of the 15 members of an adul

16. Consider an experiment that consists of determining the type of job?either blue-collar or white-collar?and the political affiliation?Republican, Democratic, or Independent?of the 15 members of an adult soccer team. How many outcomes are (a) in the sample space; (b) in the event that at least one of the team members is a b

Application of Stirling's Formula

An often used application of Stirling's approximation is an asymptotic formula for the binomial coefficient. One can prove that for k = o(n exp3/4), (n "choose" k) ~ c(ne/k)^(k) for some appropriate constant c. Can you find the c? Can you say why this only works when k is much smaller than n exp3/4?

Double Eulerian Tour

Use words to describe the solution process. No programming. 4. Suppose G is a graph. We define a double Eulerian tour as a walk that crosses each edge of G twice in different directions and that starts and ends at the same vertex. Show that every connected graph has a double Eulerian tour.

Discrete Structures : Coloring

Let G be a properly colored graph and let us suppose that one of the colours used is red. The set of all red-coloured vertices have a special property. What is it? Graph colouring can be thought of as partitioning V(G) into subsets with this special property. (See attachment for full background)

Subgraphs

Let G be a complete graph on n vertices. Please calculate how many spanning and induced subgroups G has... (see attachment)

Absolute Deviation with a Given Equation

Estimate the absolute deviation for the following calculation. List the result y and the absolute deviation. Round your answer so that it contains only significant digits. Y= 251(+/-1)*((860(+/-2))/(1.673(+/-0.006))= 129.025.70(+/-xxxxxx)

Subsequence

In a line of people you are looking for a subsequence of 4 (not necessarily consecutive = neighboring) people with increasing height. How many people should be in the line so that you can be sure to find this subsequence?

Trees

A. If T is a rooted binary tree of height 5, then T has at most 25 leaves. b. If T is a tree with 50 vertices, the largest degree that any vertex can have is 49.

Tree Traversal.

Find the: 1. preorder transversal 2. inorder transversal 3. postorder transversal Of the tree attached in the Word document.

Dimensions

We have some skylights and they measure 1.2m by 0.8m Suppose both dimensions increase by 20%. What's the percent increase in the amount of light admitted? You have a newspaper the dimensions are 35cm by 38cm they reduce the pages by 10%. There are 48 Pages in the newspaper, daily circulation of 135,000. Comp

Row operations

Using row operations, determine if the following set of equations has a solution: x1 + x2 + x3 = 3 2x1 - x2 - 2x3 = -3 3x2 - 4x3 = -3

Relations

S = {0, 1, 2, 4, 6} Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity. Also find the reflexive, symmetric and transitive closure of each relations. A) P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1), (1,2), (2,4), (4,6) } B) P {(0,1), (1,0), (2,4), (4,2), (4,6), (6,4)} C) P ((0

Cannot Work this one

In the questions below suppose the variable x represents students and the variable y represents courses, and A(y): y is an advanced course S(x): x is a sophomore F(x): x is a freshman T(x,y): x is taking y. Write the statement using these predicates and any needed quantifiers. a. There is a course that every freshman is

Palindromes

What are the palindromes between 100 & 200? Find the range, mode, and median.