Reference no: EM131026960
Q.) How would you prove the converse?
A partition of a set S defines on equivalence relation on S.
Hint: Define a relation as X - Y if X and Y are elements of the same subset of the partition.
1.) Let n be fixed positive integer greater than 1. If a mod n = a' and b mod n = b' .Prove that (a+b) mod n = (a' + b') mod n and (ab) mod n = (a'b') mod n.
2.) Let "n" be a fixed positive integer greater than 1. If a mod n = a' and b mod n = b'. Prove that (a+b) mod n = (a'+b') mod n and
(ab) mod n = (a'b') mod n.
3.) Prove that for every integer n, n3 mod 6 = n mod 6.
4.) The International Standard Book Numbers (ISBN) a1, a2,a3, a4, a5 , a6, a7,a8,a9,a10 has the property (a1, a2,....................a10) . (10, 9,8, 7, 6, 5, 4, 3, 2, 1) mod 11 = 0. The digits a10 is the check digit. When a10 is required to be 10 to make the dot product 0, the character X is used as the check digit. Verify the check digit for the ISBN assigned to this book.
5.) Let S be the set of integers. If a, b ε S, define aRb if ab > = 0. If R an equivalence relation on S?
6.) Let S be the set of integers. If a, b ε S, define aRb if a + b is even. Prove that R is an equivalence relation and determine the equivalence classes of S.
Casualty of a down economy by declaring bankruptcy
: In 2007, Lehman Brothers Holdings, Inc. became a casualty of a down economy by declaring bankruptcy. The federal government of the United States offered no intervention and permitted the company to fail.
|
Find the amount of tax for a single taxpayer with taxable
: The value of the expression 4220 + 0.25(x - 30,650)is the 2006 federal income tax for a single taxpayer with taxable income of x dollars, where x is over $30,650 but not over $74,200.
|
Urine flows through the urinary system in which order
: Which of the following organs removes bilirubin from the blood, manufactures plasma proteins, and is involved with the production of prothrombin and fibrinogen?
|
How sustainable is sustainable tourism
: How sustainable is sustainable tourism - Are capitalism and conservation compatible and examination of the implications of radically reducing oil dependency.
|
How would you prove the converse
: Let S be the set of integers. If a, b ε S, define aRb if a + b is even. Prove that R is an equivalence relation and determine the equivalence classes of S.
|
What is the average velocity if the diameter changes to six
: What is the average velocity if the diameter changes to 6 in.? b. Express the average velocity in terms of an arbitrary diameter.
|
What are the dimensions of the photo
: A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally.
|
Estimate the number of decimal digits of the keys
: Write a reflection report in 100 words about the role of cryptography in securing communication of confidential documents - Encrypt a file and output the cipher text in ASCII format.
|
Prepare a contribution format income statement
: Prepare an income statement for the month using absorption costing.
|