Please solve this with detailed reasoning

2. Consider the following theorem: (20pts) "For an integer n, if n is odd, then n3 is odd." (a) Verify that the theorem is true using direct proof. (b) Prove the Converse of the theorem. 3. Prove or Disprove the following statements: (20pts) (a) For any two different rational numbers, there's another rational number strictly between them. (b) The product of two irrational numbers is an irrational number. (c) For real numbers a and b, if a>b then a2>b2 (d) For every non-zero real number x, if x is irrational, then 2x+1 is also irrational