For problems #1 through 6, prove the given statement. I. For all integers n, if n is odd then is odd. 2. If n is any odd integer, then (1)"1 3. For al positive integers k, F + 2k + 1 is composite. 4. If a is any odd integer, then a'+ a is even. 5. There is an integer n such that 2n2-5n + 2 is prime. 6. For all integers a, b,and c, if a l b and a | c, then a | (b-c) For problems #7 through 10, determine whether the given statement is true or false. If true, provide a proof, if false, provide a counterexample. 7. There exists an integer k2 4 such that 2k2-5k+ 2 is prime. 8. For all integers n and m, if n-m is even then n-mr3 is even. 9. For all integers a, b,and c, if a | bc then a lb or a| c 10. A necessary condition for an integer to be divisible by 6 is that it be divisible by 2