5. Prove for all real numbers x and y, if x-[x ]

5. Prove for all real numbers x and y, if x L x then 6. Use proof by contradiction to show that for every real number r, if r2 is irrational then ris irrational. 7. Use proof by contraposition to show that for all nonnegative real numbers x and y, if x and y are positive then 8. Use proof by contradiction to show that for all integers a, b, and c, if a divides b and a does not divide c then a does not divide b + c.