Directed Graphs & Binary Relations

A = [ 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 ] Compute the reachability matrix R by using washall's algorithm and also by using the formula R = A V A(2) V... V A(n)

I have three I cannot get

I have done several examples but these I cannot get right, I am not sure where I have made the mistake and I am confusing myself. a. List all the binary relations on the set {0,1}. b. List the reflexive relations on the set {0,1}. c. List the symmetric relations on the set {0,1}.

Counting

a. An office manager has four employees and nine reports to be done. In how many ways can the reports be assigned to the employees so that each employee has at least one report to do. b. Find the number of ways to put eight different books in five boxes, if no box is allowed to be empty.

Percents

A. You take a job that pays $25,000 annually. (a) How much do you earn n years from now if you receive a three percent raise each year? (b) How much do you earn n years from now if you receive a five percent raise each year? (c) How much do you earn n years from now if each year you receive a raise of $1000 plus two per ...continues

Random

In the questions I have below it says a bowl has eight ping pong balls numbered 1,2,2,3,4,5,5,5. You pick a ball at random. a. Find p(the number on the ball drawn is ≥ 3). b. Find p(the number on the ball drawn is even).

Seem like these are more statistical

a. How many permutations of the seven letters A,B,C,D,E,F,G are there? b. You have a pile of 20 identical blank cards. On each card you draw a circle, a plus, or a square. How many piles of 20 cards are possible? c. Find the next four largest 4-combinations of the set {1,2,3,4,5,6,7,8} after {1,2,3,5}. d. What is th ...continues

Prove the follwoing

Show that every positive integer can be written as the product of two numbers. One is the power of 2 and one is odd.

Integers

suppose that integers 1,2,3,4,5,6,7,8,9,10 are arranged randomly along a circle. 1) show that For each circular arrangement, there exists at least three adjacent numbers whose sum is greater than 17 2) take n + 1 integers from {1,2,3,....., 2n}. Show there exist two integers, one divides the other completely.

Divisibility

Suppose A divides N and B divides N. Does this always imply: A * B divides n? Now the question is under what condition A*B will always divide N? Prove it.

Fibonacci sequence

Please look at the attached file