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Sets - List the elements in the set.1

Write the word or phrase that best completes each statement or answers the question. List the elements in the set. 1. Let U = { q,r,s,t,u,v,w,x,y,z} A = { q,s,u,w,y} B = {q,s,y,z,} C = { v,w,x,y,z} a. (A INTERSECT B') U (B INTERSECT A') B. A'-C Use the formula for the number of subsets o

Relations and sets

1) Find a relation R on a set S that is neither Symmetric nor antisymmetric 2) Let S be a set containing exactly n elements. How many antisymmetric relations on S are there. 3) give a recursive definition of X^n for any positive integer n 4) give a recursive definition of the nth odd positive integer 5) Let g: Z -> Z

Counting and subsets

Use the formula for the number of subsets of a set with n elements to solve the problem. 1. Pasta comes with tomato sauce and can be ordered with some , all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli,shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for

Permutations and combinations..

In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components,in a manner that minimizes the impact of shocks. One end of the casing is designated as the top and the other end the bottom. a) how many different designs are possible b) If the seven compon

Counting Bitstrings

How many bitstrings of length 10 are there that contain 5(or more) consecutive 0's or contain 5(or more) consecutive 1's? Justify your answer.

Standard Combinatorics

Problem 1) We have 20 kinds of presents; and we have a large supply of each kind. We want to give presents to 12 children. It is not required that every child gets something; but no child can get 2 copies of the same present. In how many ways can we give presents? Problem 2) List all subsets of {a,b,c,d,e} containi

Combinatorics Color Objects

Problem1) What is the number of ways to color n objects with 3 colors if every color must be used at least once? problem2) prove that for any three sets A,B,C ; ((AB) U (BA))^ C = ((A^C) U (B^C)) (A^B^C) ^ means intersection Please explain the steps, help me under

Counting and Combinations

Problem 1) How many bits does 10^100 (ten power one hundred) have if written in base 2? problem 2) Find the number of all 20-digit integers in which NO two consecutive digits are the same Please explain to me the steps, don't just give me the answer, thank you very much.

Combinations of Letters and Digits

Could someone show me how to solve the following. 20. 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?

Set Partitions and Bit Strings

Which of these collections of subsets are partitions on the set of bit strings of length 8? a) The set of bit strings that end with 00; the set of bit strings that end with 01; the set of bit strings that end with 10; and the set of bit strings that end with 11. b) The set of bit strings that end with 111; the set of bit

Union and Intersection of Sets

Create 2 sets. Set A will be the list of the 5 items you personally need to buy the most (essential items). Set B will be the list of 5 items that you want to buy the most ( fun stuff). List the items in set A and B and also list or state the items in the union and in the intersection of set A nad B Assume that the prices of

Solving a Combinations Problem

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 either solid white or green. Juan painted his cube with all six faces white. Julie painted her cube solid green. Herman painted 4 faces white and 2 faces green. How many cubes could be paint

Abstract Algebra : Permutations, Binary Operations and Mappings

Consider a non-empty set A. Prove that S(A) is closed in (M(A),o). Meaning: "o" is the composition of functions which defines a binary operation on M(A), the set of all maps from A to A. You need to prove that the set of all permutations on A is closed under the composition.


A representative of the Environmental Protection Agency wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?

Set Operations

1. Write the following in roster form: Set N is the set of natural numbers between ten and sixteen 2. Express the following in set builder notation: Z = {2, 3, 4, 5, 6, 7, 8, 9, 10} 3. For sets A and B, determine whether A = B, A is a subset of B, or B is a subset of A

Interval Notation Question

Write the sets attached using interval notation. If the set is empty, write O. a) The intersection of D and C, where D = {x|x <= -3} and C = {x|x >= 2}. b) {x|x < 3 and x >= 4}

Vertices, Nodes, Breadth-First Search Algorithm and Rooted Trees

1. Use the breadth first search algorithm to find a spanning tree for the following connected graph. Start with A and use alphabetical order when there is a choice for a vertex. 2. For the following rooted tree, identify the following: (a) Which node is the root? (b) Which nodes are the internal vertices? (c) Is th

Combinations Expansion Subsets

1. The coefficient of x^7y^2 in the expansion of (2x-y)^9 2. How many subsets of {2,3,5,7,11, 13, 17,19,23) contain four numbers? 3. If a committee varies its meeting days, how many meetings must it schedule before we can guarantee that at least two meetings will be held on the same day of the week?? 4. How many differe

How Combinations Are Determined

A woman has 9 close friends. (a) In how many ways can she invite five of these to dinner? Explain/show work. (b) Repeat part (a) with the added stipulation that two of her friends do not like each other so that if she invites one of them she cannot invite the other. Explain/show work. (c) Repeat part (a), assuming t