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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.
Sorting given an array with 100,000 entries to sort. Under what circumstances would you use each of the following: insertion sort,mergesort'quicksort
Write a program that asks for purchase price and to calculate, state sales tax, county sales tax and then display purchase price, both sales tax amount and then the total.
The following program will display an integral solution to the quadratic equation ax2+bx+c for integral values of a,b, and c, where a,c fall between 0 and 10, while b falls between 1 and 1000.
Writer a program that allows the user to enter an unknown number of characters, stores those characters in a data structure (a vector) and then prints the values to the screen.
For example, 6 is a perfect number because 6 = 1 + 2 + 3. Write a Java program that decides whether integer is a perfect number.
Create a class named Student that has three member variables
Alicia creates a button using the code JButton exitButton = new JButton("exit"); and places it into a JFrame named mainFrame
What is a JFrame? Describe the usefulness of the JFrame class
It is usually unnecessary or not feasible to maintain a constant media schedule all year. What are the two other alternatives and what key characteristics of these two alternatives would be taken into account?
Create a computer class and assume computers have the following fields: String manufacture, double price, int year
write an applet that displays a 4x4 grid. when the user clicks on a square in the grid the applet should draw a filled
Write an application that plays "guess the number" as follows: Your application chooses the number to be guessed by selecting an integer at random in the range 1-1000. The application then displays the following in a label
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