USE PROOFS TO COMPLETE BELOW QUESTIONS 1. DIRECT - Prove that the product of two odd natural numbers must be odd. DIRECT -Prove that if n is an even natural number and if m is any natural number then n m must be even. Use the method of induction to prove that, for every natural number n, the number n+ 2. 3. 5n +6 is even. 4. DIRECT-Prove that the square of an even natural number is even. 5. Induction- Prove that, if n is a positive integer, then the quantity n2+3n +2 is even. 6. DIRECT-Prove that the square of an odd natural number is odd. 7. DIRECT-Prove that the cube of an odd number must be odd. 8. DIRECT -Show that the sum of two odd natural numbers is even. 9. DIRECT-Prove that the sum of an even integer and an odd integer is odd. 10. DIRECT-The sum of two even natural numbers is even. 11. Proof by cases-Using conditionals, if antecedent if false, then truth value will always be TRUE