10. (10 points) In this problem, we will prove the following statement: For all integers n, if (n + 1)2 is an even number, then n is an odd number. i. Write the contrapositive of the above statement. Your answer should include a quan- tifier or the appropriate use of the words "for all" or "there exists". ii. Prove the original statement by contrapositive, not by contradiction! For this problem, I expect to see the following, at minimum: Use complete sentences throughout your proof. Define any variables you use, and stating which set they come from (c.g. R, Q, Z, N, etc.), and explaing your arguments thoroughly using definitions where necessary. . Make sure your proof ultimately satisfies the claim you are trying to show. End your proof with a square, or any other appropriate celebratory symbol that you like! 10. (10 points) In this problem, we will prove the following statement: For all integers n, if (n + 1)2 is an even number, then n is an odd number. i. Write the contrapositive of the above statement. Your answer should include a quan- tifier or the appropriate use of the words "for all" or "there exists". ii. Prove the original statement by contrapositive, not by contradiction! For this problem, I expect to see the following, at minimum: Use complete sentences throughout your proof. Define any variables you use, and stating which set they come from (c.g. R, Q, Z, N, etc.), and explaing your arguments thoroughly using definitions where necessary. . Make sure your proof ultimately satisfies the claim you are trying to show. End your proof with a square, or any other appropriate celebratory symbol that you like