12 and 28 (with contradiction please)

ad integer if ana, is an odd inte en integer if and counterexample to the following statement: The number counterexample to the following statement: The number n is an even into multiple of 4. rer, so x + y = 2m + 4. Provide countele a. Ifa and bare integers where a b. If '>0 then > 0. 2+1 is prime. c. If is an even number, then ar + 1 is prin d. If n is a positive integer, then > ml. 5. Provide a counterexample to 3 + 5 is an even integer. 6. Provide a counterexample to the following statem 3n+2 is an even integer. 7. a. Find two even integers whose sum is not a multiple of two even numbers is a multiple b. What is wrong with the following proof" that the sum 2m and y = 2m, where is an integer, SO x + y = 2 randy be even numbers. Then which is an integral multiple of 4. 8. a. Find an example of an odd number x and an even numbe and an even number y such that x - y = 7. dd number minus an even number is als b. What is wrong with the following proof that an odd num re m is an integer, and x - y = 2m + Letxbe odd and y be even. Then r = 2m + 1, y = 2m, where it is an For Exercises 9-46, prove the given statement. is a perfect square and is a sum of two perfect squares. - If n = 25, 100, or 169, then 10. If n is an even integer. 4 Sa 12. then n is a sum of two prime numbers. 11. For any positive integer n less than or equal to 3, n! . 28. If x2 + 2x - 3 = 0, then x + 2. 29. If n is an even prime number, then n = 2. 30. The sum of three consecutive integers is divisible by 3. 31. If two integers are each divisible by some integer n, then t 32. If the product of two integers is not divisible by an intege 33. If n, m, and p are integers and n m and mp, then n p. 34. If n, m, p, and q are integers and n p and mq, then nm 35. The square of an odd integer equals 8k + 1 for some in 36. The sum of the squares of two odd integers cannot be a 37. The product of the squares of two integers is a perfect 38. The difference of two consecutive cubes is odd. 39. For any two numbers x and y, (x + y = x + \yl. 40. For any two numbers x and y, xy = |v|| yl. Louerage of the n numbers X1, X2