i need help with 6(b,h), 7(b,d,f), and 8(d).

6. (False Converses) Write down the converse of each conditional statement about the integers. Then give a reason why the converse is false. a. If x > 0 and y > 0, then x + y >0. b. If x is odd and y is odd, then x + y is even. c. If x divides y, then x divides 3y. d. If x is even and y is odd, then xy is even. 7. Prove or disprove each of the following statements by exhaustive checking, a. There is a prime number between 45 and 54. b. The product of any two of the four numbers 2, 3, 4, and 5 is even. c. Every odd integer between 2 and 26 is either prime or the product of two primes. d. If dab, then dla or dib. e. If m and n are integers, then (3m + 2)(3n + 2) has the form (3k + 2) for some integer k. f. The sum of two prime numbers is a prime number. g. The product of two prime numbers is odd. h. There is no prime number between 293 and 307. 8. Give a direct proof for each of the following statements about the integers. a. If x and y are even, then x + y is even b. If x is even and y is odd, then x + y is odd. c. If x and y are odd, then x - y is even d. If x is odd and y is odd, then xy is odd. e. If xly and y is odd, then x is odd