7. Suppose a,beZ. If both ab and a +b are even, then both a and b are even. 4. Suppose a,b,c € Z. If a does not divide be, then a does not divide b. 2. Suppose ne Z. If n2 is odd, then n is odd. 3. Suppose a,be Z. If a (b² -2b) is odd, then a and b are odd a 5. Suppose x ER. If x + 5x<0 then x<0. 6. Suppose x ER. If x-x> 0 then x>-1. 8. Suppose x €R. If x - 4x*+3x3 -x2 + 3x - 420, then x20. 9. Suppose n e Z. If 3{n2, then 3 n. 10, Supposex,y,z €Z and x#0. If x{yz, then xy andx z. 11. Suppose x,y€ Z. If x²(y+3) is even, then x is even or y is odd. 12. Suppose a € Z. If a? is not divisible by 4, then a is odd. 13. Suppose x€R. If x+7x³ + 5x >x* +x2 + 8, then x > 0. B. Prove the following statements using either direct or contrapositive proof 14. If a,beZ and a and b have the same parity, then 3a +7 and 76 -4 do not. 15. Suppose xe Z. If x – 1 is even, then x is odd. 16. Suppose x,y € Z. If x+ y is even, then x and y have the same parity. 17. If n is odd, then 8| (n2 – 1). 18 If a,beZ, then (a+ b)³ = a³ + b³ (mod 3). 19. Let a,b,CeZ and neN. If a = b (mod n) and a = c (mod n), then c =b (mod n). 20. If a eZ and a = 1 (mod 5), then a² = 1 (mod 5). 21. Let a,be Z and ne N. If a =b (mod n), then a = 63 (mod n). 22. Let a e Z, neN. If a has remainder r when divided by n, then a =r (mod n). 23. Let a,be Z and neN. If a =b (mod n), then a2 = ab (mod n).