代写Mathematics调试数据库编程

1. Using proof by contrapositive,show that if a andb are integers and √3 is rational, then b/a ≠ √3 [15 pts]

2. Using proof by contradiction,show that there is no greatest integer.                              [15 pts]

3. Using proof by contradiction,show that if n² is divisible by 4,then n is divisible by 2.[15 pts]

4. Suppose n ∈ Z.Prove the following statement: 5n + 3 is odd if and only if n is even.[15 pts]

5. For each of the following statements,determine whether it is true or false. If true, provide a proof. If false disprove it.

(a)Suppose x ∈ R. Then  |x| = 3  if  and   only  if  x = 3   or x = -3. [5 pts]

(b)Suppose x ∈ R. Then x² = 9  if and  only  if x = 3. [5 pts]

6. Prove or disprove the following statement:For any two different rational numbers,there's another rational number strictly between them.       [15 pts]

7. Prove by contradiction that 6x³ + 8x + 1 = 0 has no integer solutions.                           [15 pts]