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Discrete Structures

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)


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)


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?


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.


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


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


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

Equivalence Relations and Classes

Let L be a subset of {a,b}* Define a relation R (R sub L) on S* as follows: L for All of x, y is a member of S*, (x,y) are members of R if for all of z, xz are members of L iff yz are members of L A) Show that R is an equivalence relation B) Suppose L={a^i b^i where i >= 0} What can you say about the inde

Discrete Math: Logic and Directed Graphs

Please see the attached file for the fully formatted problems. 1. Circle T for True or F for False as they apply to the following statements: T F Every compound is either a tautology or a contradiction. T F Integers are Rational. T F The empty set has no subsets. T F Onto functions map smaller sets to bigger sets. T F

Domination number

Determine (without proof) a formula for the domination number of path Pn.

Discrete Structures

11) Use generating functions to determine the number of different ways 12 identical action figures can be given to five children so that each child receives at most three action figures. 12) Use generating functions to find the number of ways to select 10 balls from an urn containing red, white and blue balls if: a. The

Discrete structures

6. A string that contains only 0s 1s and 2s is called a ternary string a) find a recurrence relation for the number of ternary strings that contain two consecutive 0s b) what are the initial conditions c) how many ternary strings of length six contain two consecutive 0s The next 3 problems deal with a variation of the

Standard deviation calculation by frequency table

Find the standard deviation of the data in the given frequency table. A company had 80 employees whose salaries are summarized in the frequency table below. Find the standard deviation. Salary Employees 5001-10000 17 10001-15000 16 15001-20000 20 20001-25000 15 25001-30000 12