1. The sum of two odd integers is even.2. The sum of two even integers is even.3. The square of an even number is even.4. The product of two odd integers is odd.5. Ifn3+ 5 is odd thennis even, for anyn∈Z.6. If 3n+ 2 is even thennis even, for anyn∈Z.7. The sum of a rational number and an irrational number is irrational.8. The product of two irrational numbers is irrational.9. Use mathematical induction to prove that the firstneven integers add up ton(n+ 1)10. Use mathematical induction to prove thatn3+ 2nis divisible by 3.