Name: Learning Objective 9 Homework Due at the start of class on Friday, March 13. MAT...

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Name: Learning Objective 9 Homework Due at the start of class on Friday, March 13. MAT 224, Spring 2020 Please clearly write your solutions on a separate piece of paper. Be sure to show all your work. Multiple pages must be stapled. Learning Objective 9: Be able to use logical equivalencies to prove statements. This includes, but is not limited to, the contrapositive and biconditional. 4. Prove the following: 1. Let a, b and e be integers. Prove that if at be, then a tb or ate. 2. Let a be an integer and let n be a natural number. Prove that a 0 (mod n) if and only if n/a. 3. Prove the following: For all integers a and b, if ab is even, then a is even or b is even. Let z be an integer. Prove that 52-11 is even if and only if r is odd. Name: Learning Objective 9 Homework Due at the start of class on Friday, March 13. MAT 224, Spring 2020 Please clearly write your solutions on a separate piece of paper. Be sure to show all your work. Multiple pages must be stapled. Learning Objective 9: Be able to use logical equivalencies to prove statements. This includes, but is not limited to, the contrapositive and biconditional. 4. Prove the following: 1. Let a, b and e be integers. Prove that if at be, then a tb or ate. 2. Let a be an integer and let n be a natural number. Prove that a 0 (mod n) if and only if n/a. 3. Prove the following: For all integers a and b, if ab is even, then a is even or b is even. Let z be an integer. Prove that 52-11 is even if and only if r is odd.

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1 Proof Let a b and c be integers To prove that if at be then ab or ate we must show that if the statement is true then the conclusion follows Assume ... View the full answer