1. Prove that the difference of two odd integers is even. Give a justification at each step.2. Prove that the sum of any two rational numbers is a rational number. Give a justification at eachstep.3. Prove by contradiction that there is no greatest integer.4. Prove by contraposition that for all integers n, if n2 is even then n is even.5. Prove using mathematical induction: ∀ integers n ≥ 1, 2 + 4 + ... + 2n = n2 + n. Give justificationsfor each step.