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Let G be a transitive permutation group on the finite set A with |A|>1. Show that there is some g in G such that g(a) is not equal to a for all a in A.
Use the breadth-first search algorithm to find a spanning tree for the following connected graph. Start with A and use alphabetical order.
Without writing them down what are the number of subsets of the set A = {a, b, c, d, e, f}? Of set B = {a, b, c, d, e, f, g, h, i, j}?
A sinking fund is established to obtain $75,000 in five years. The interest rate is 10% and payments are made quarterly.
The parentheses in R(x) is used to distinguish the ring R(x) of rational functions from the ring R[x] of polynomials.
Assuming that the nine friends consist of five single people and 2 married couples. If she invites a husband or wife she must invite the spouse.
If alpha is an r-cycle, show that alpha^r = (1). [There's a hint that If alpha = (i sub 0 ... i sub r-1), show that alpha ^k(i sub 0) = i sub k.]
A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different meals consisting of one salad, one main dish.
In how many ways can a six-letter security password be formed from letters of the alphabet if no letter is repeated?
Let S be a set of people. For x, y E S, define xRy to mean that x = y or x is a decendant of y. Prove that R is a partial order on S.
A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation,no engines, one engine, two engines.
In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components.
To prevent false alarms, the system is designed so that three or more of the sensors must sense over temperature before a warning signal is given.
How many different license plates can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits?
The set of bit strings that end with 111; the set of bit strings that end with 011; and the set of bit strings that end with 00.
Mrs. Jones had some white paint and some green paint, and a bunch of wooden cubes. Her class decided to paint the cubes by making each face.
Meaning: "o" is the composition of functions which defines a binary operation on M(A), the set of all maps from A to A.
Given U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, m, n, o, p, q}, B = {n, o, r, s, v, w}, and C = {l, m, p, q, r, t}, find (A' U C') n B'.
A representative of the Environmental Protection Agency wants to select samples from 10 landfills.
An automobile manufacturer produces 7 models, each available in 6 different exterior colors, with 4 different upholstery fabrics and 5 interior colors.
A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation, no engines , one engine.
Prescribe a grand strategy for the organization. Explain the reasons for your recommendation.
There are two small towns, Greenville and Yellowville. Greenville contains 20 houses and Yellowville contains 15 houses.
Describe (in words) two different sets of people containing you as a member. Describe (in words) the complement of each set.
There will always be a 1 foot by 1 foot by 1 foot gap somewhere. In how many ways can this gap be in the interior of the blocks and not on an outside surface?