Hi I need help on what is the answer to this problems? Below is the question and other concerns will be in the comment section. I hope you can help me and surely I will give you full positive feedback.

I. Prove or Disprove. Write a short proof if the given statement is always true. Otherwise, provide a counterexample. 1. If n is an integer, then 2n + 1 is odd. 2. The square of any integer can be written in the form 3k or 3 + 1, for some ke Z. 3. Let a and y be positive integers. If a divides y and y divides r, then r = y. 4. Let a, b, ce Z. If c divides a + b, then c divides both a and b. II. Do as indicated. 1. Use PMI to show that for any n E N, 4 divides 5" - 1. 2. Prove that v3 is irrational