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1. Prove that the difference of two odd integers is even. Give a justification at each step.
2. Prove that the sum of any two rational numbers is a rational number. Give a justification at each step.
3. Prove by contradiction that there is no greatest integer.
4. Prove by contraposition that for all integers n, if n2 is even then n is even.
5. Prove using mathematical induction: ∀ integers n ≥ 1, 2 + 4 + ... + 2n = n2 + n. Give justifications for each step.
6. Explain the difference between proof by contradiction and proof by contraposition. Give an example of a theorem that would lend itself to proof by contradiction. Explain why that proof technique would be a good choice in this case.
Create a project that would let a user compute area and perimeter of a polygon
Your code will prompt the user to enter a file name. If this file does not exist the program will produce an error message and exit. Otherwise the program will open the file and read a line from the file, reverse the line, and then print the line to ..
Write a program to compare Berlin, Tehran and Seoul information with Louisville - Your program should ask the User to select one of the cities with entering their first letters as input, "B" for Berlin, "T" for Tehran and "S" for Seoul.
Write a Bag class with a generic type. Write a class such as item that has a name and price. Add objects of item to the bag and find the average and the total of the price of all items in the bag.
The birthday paradox states that if there are 23 people in a room then there is a slightly more than 50:50 chance that at least two of them will have the same birthday.
Each class is simply a wrapper class to hold a private array variable. int [] a; The default constructor for each class should initialize â??aâ??. Each class should have a toString() and equals(). Each class should have a setArray method that allows ..
Write a Java program that satisfies the given requirement - Prompts the user to input exactly nine characters, which constitute a valid lock combination.
You need a java program to compute the invoice for client and then print out invoice to the screen. The consulting rate is $200 per hour.
Do not define an input method. The only method that can set the counter is the one that sets it to zero. Write a program to test your class definition.
Code a while loop that keeps printing "You are a DEDICATED student!" as long as the user enters an attendance rate of 90% or greater. Assume the loop-control variable, attendance, is already declared along with input for the Scanner class. The w..
Can a person who has a criminal conviction open a business as a sole trader?
Create an interface called Player. The interface has an abstract method called play() that shows a message describing the meaning of "play" to the class.
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