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# Recurrence Relation

### Prove theta Relation : Reflexive, Symmetric and Transitive

Prove that theta is a reflexive, symmetric, and transitive relation; that is for all f, g, h: N to N, a. f belongs to theta f; b. f belongs to theta g then g belongs to theta f; c. f belongs to theta g and g belongs to theta h then f belongs to theta h;

### DETERMINE THE DOMAIN AND RANGE OF EACH RELATION

_______ Y =&#8730; X - 2 _________ Y = &#8730; X + 4 ___ Y= &#8730; 2X _______ Y= &#8730; 2X - 1

### Recurrence Relation

Find and prove a closed form for the recursion X_0 = 1, X_n = 3X_(n-1) - 1

### Probability : Mean, Standard Deviation and Recurrence Relation

In order to test a vaccine, we have to find patients with a certain blood type, that is found in 20% of the population. Model W, the number of people sampled until we have found one with thhis blood type; X, the number sampled to find four with the blood type; and Y, the number with this blood type among 20 people. Find the mean

### Domain and Range of a Relation

1. Find the domain and range of the relation {(x,y)&#9474;5x < -5} 2. Find the domain of the relation A={(x,y)&#9474;x^2+y^2=4}

### Joint Mass Function, Forming a Triangle and Recurrence Relation

Suppose the joint mass function of X and Y, the numbers of goals scored by home and away teams in a soccer league is as shown in the below table... Another way in which a stick might be broken "at random" is to independently Select random points in each of the two halves. What would be the chance of the three pieces forming

### Equivalence Classes for Relation on N

5b. Describe the equivalence classes for the following relations on N. x~y iif x mod 2 = y mod 2 and x mod 4 = y mod 4

### Curls : Green's Theorem

When I write A_n it means A "sub" n. a) Define A_n= integral from 2pi to 0 of (Cos(theta))^(2n).d(theta) Proove the recurrence formula(*): A_n=(2n-1)/(2n)*A_(n-1) by writing Green's thorem for vector field F=x^(2n-1)j in the unit disc x^2+y^2<1 and evaluating each of the integrals sepa

### Solving a Recurrence Relation

Solve the following recurrence relation: a(n) = a(n-1) + 3(n-1), a(0) = 1 I know this should not be a difficult problem, but my main problem is in solving the problem when the coefficient of the a(n-1) term is 1. Also, when a summation is in the solution, I do not understand how to convert from a summation to a C(n,k)

### Solving recurrence relations.

Find and solve a recurrence relation for the number of ways to make a pile of n chips using red, white, and blue chips and such that no two red chips are together.

### Relations: Properties and Equivalence Classes

Please see the attached file for the fully formatted problem. Exercise 5 (4p) R is the relation defined on Z ts follows: for all m,n E Z, m R n <=>4|(m-n) a. Determine whether the relaition is reflexive. b. Determine whether the relation is symmetric. c. Determine whether the relation is transitive. d. In case the relat

### Equivalence Class Relations

Let P, P' be equivalence relations on a set A. Let n, n' be the number of equivalence classes of p, p', respectively. A) define an equivalence relation p'' as follows: xp''y <=> (xpy) and (xp'y) what is the least number of equivalence classes of p''? What is the greatest number of equivalence classes of p''? B)defin

### Prove recurrence relationship of Catalan Numbers.

Prove recurrence relationship of Catalan Numbers. Question: Let n be a non-negative integer. The number, x[n], of topologically distinct binary trees with n nodes can be shown to satisfy the following recurrence (x = 1): See attached file for full problem description.

### Equivalence Relations and Class

Verify that each of the following are equivalence relations on the plane R^2 (where R are real numbers) and describe the equivalence classes geometrically. 1) (x1,y1)R(x2,y2) if and only if x1 = x2 2) (x1,y1)R(x2,y2) if and only if x1 + y1 = x2+y2 3) (x1,y1)R(x2,y2) if and only if x1^2 + y1^2 = x2^2 + y2^2.

### Mathematical Induction - Fibonacci Recurrence

Prove that the Fibonacci sequence can be obtained by the recurrence relationship. See attached file for full problem description.

### Fibonacci sequence in closed form

Prove that Fn can be expressed by: Fn=[(a^n-b^n)/(a-b)] for n=1,2,3... ~: Set Gn=[(a^n-b^n)/(a-b)] and show that Gn satisfies the recurrence formula {G(n+1) = Gn + G(n-1) for n=2,3,4...} and don't forget that a and b satisfy the equation x^2-x-1=0. a and b are the roots of x^2-x-1=0, which are (1+sqrt5)/2 and (1-sqrt5)/2

### Discrete Structures

1. Consider the sequence of triangles Ti, i >= 2: T2 is simply a triangle sitting upright, on its base. T3 is T2, except that an additional straight line is drawn from the upper vertex, down to somewhere on the base. For each Ti+1, one more line is added to triangle Ti (such that each line meets the base at a different point).

### Writing recursion formulas.

An = 1/2n. Write the recursion formula for this series?

### Working with second order linear homogeneous recurrence relations

Suppose a sequence satisfies the given recurrence relation and initial conditions. Find an explicit formula for the sequence s(subk)=-4s(subk-1)-4S(subk-2), for all integers k>or equal to 2 s(sub0)=0,S(sub1)=-1