Name: Math 2300, Spring 2024 - Discrete Structures Quiz 3 All answers must be your own work. You may use both sides of one 8.5x11 inch paper that you made yourself (your handwriting). To receive full credit, show your work, justify, explain and write legibly. There are 4 problems on 2 pages. You may not use contradiction for any of these proofs. 1. Prove that the product of an even integer and an odd integer is even 2. Prove: For all integers a, b, and c, if a | b and a | c, then a | (13b-7c).3. Claim: For all integers a, b. and c. if a | (b+c). then a | bora | c. a. To show the claim is false, we can show that the negation is true. Write the negation: b. To show the negation is true, find a numeric example and carefully check it, explaining what you are doing 4. Let n be an integer. Prove that if w is odd, then n is odd