Exercise 7. Is the the argument below valid? Justify your answer. 3x(Z(z) ? F(z)) Exercise 8. Given that?E Z, prove that z2-z is an even integer. Exercise 9. Let z, y Q'. Prove that 5r +2y e Exercise 10. Prove or disprove: If Q then Q Exercise 11. Prove by contradiction that if r E Q. and s Q then r Q Exercise 12. By direct proof, show that if a+b+ab 0 then a-b-2 where a, b e Z e Q 3y Exercise 13. a) Let m, n E Z, and suppose that n2+1 2m. Prove that m is the sum of the squares of two integers. b)Write 9,561,565 as the sum of two squares. Note that 43732 +1-2 x 9,561, 565 Exercise 14 a) Give a direct proof of the fact that a2 -5a+6 is even for any integer a b) Suppose a, b E Z and a2 -5b is even. Prove that b -5a is even