Trees

Unless you are confident please do not accept 1.Use the depth-first search numbering obtained in the indicated exercise to list the back edges in the graph. Use the file (5.3jpg) 2. Use Prim's algorithm to find a minimal spanning tree for each weighted graph. (Start at A) Give the weight of the minimal spanning tree found ...continues

A binary relation R is defined in terms of a given matrix. Determine whether R is a partial order. If it is, draw its Hasse diagram.

For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R: ---------------------------------------- Row 1: 1 0 1 Row 2: 1 1 0 Row 3: 0 1 1 ----------------------------------------- Determine whether R is a partial order. If it is, draw its Hasse diagram.

This problem introduces basic axioms of probability. The idea of intersection and union are examined. Simple examples are used to illustrate these ideas.

Q: Let A and B be two events defined on a sample space S such that P(A)=0.5 P(B)=0.25 P(A or B)=0.7 [P(A union B)=0.7] Find the following (1) P(A and B) [P(A intersect B)] (2) P(A^C and B) [P(A complement intersect B)] See word document for a cleaner version of the problem.

pi=(245)(1354)(125). Write as product of disjoint cycles. What's pi^2, pi^5,pi^(-1)?

In S(5) let pi=(245)(1354)(125). Write pi as a product of disjoint cycles and then answer the following questions. (a) Determine pi^2, pi^5, pi^(-1). (b) What is the order of pi? Why?

Proof methods & strategy

I'd like to know how I can find a solution for this type of problem, I have to answer some that are similar to it but I don't understand this practice problem. Problem: Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

Functions

I need help figuring this problem out because I'm going to have to take a quiz that has similar problems, I tried to do it based on my class notes and reading but now I'm confused.

Sequences & Summations

I need help with finding the solution to this problem, I did it but I don't think what I did it right. I need to know how to do this type of problem because I'm going to have a quiz that is going to cover this type of questions.

Matrices - Find the product AB for total of 3 pairs of matrices.

Find the product AB, where a) A = [] B = [] b) A = [] B = [] c) A = [] B = [] (Please see the attached file to view the questions)

Complexity of algorithms

How much time does an algorithm take to solve a problem of size n if this algorithm uses 2n^2 + 2^n bit operations, each requiring 10^-9 second, with these values of n? i) 10 ii) 20 iii) 50 iv) 100 I need help with a question, the attachment contains the question as well as what I think is the answer. Could someone ple ...continues

Mathematical Induction

I need help figuring out a problem that for some reason I just can't quite figure out. So I found one similar to the one I can't figure out. I'd like to know which steps I need to follow in order to solve the following type problem. Prove that 3^n < n! if n is an integer greater than 6