# What is the first line of the proof

• Slides: 7

What is the first line of the proof? 1. If a divides b, then a divides b – c. 2. If a divides b, then a divides c. 3. Assume a divides b – c. 4. Assume a divides b and a divides c. 5. Assume a does not divide b and a does not divide c.

What is the next line of the proof? 1. Then a must divide b – c. 2. Then a does not divide b – c. 3. Then b = ka and c = ka for some integer k. 4. Then b = ka and c = ja for some integers j and k. 5. Then a = kb and a = kc for some integer k. 6. Then a = kb and a = jc for some integers j and k.

What is the next line of the proof? 1. Then b – c = ka. 2. Then division is distributive so a divides b – c. 3. Then a divides b – c. 4. Then k – j = … 5. Then b – c = … 6. Then a = …

What is the first line of the proof? 1. Assume a divides c. 2. Assume c divides a. 3. Assume a divides b and b divides c. 4. Assume b divides a and c divides b. 5. Assume a does not divide b and b does not divide c. 6. Assume a does not divide b or b does not divide c.

What is the next line of the proof? 1. Assume xy is odd. 2. Assume xy is even. 3. Assume x and y are both odd. 4. Assume x and y are both even. 5. Assume x or y is odd. 6. Assume x or y is even.

What is the next line of the proof? 1. Assume xy is odd. 2. Assume xy is even. 3. Assume x and y are both odd. 4. Assume x and y are both even. 5. Assume x or y is odd. 6. Assume x or y is even.

What is the next line of the proof? 1. Then x = 2 m and y = 2 m for some integer m. 2. Then x = 2 m and y = 2 n for some integers m and n. 3. Then xy is even. 4. Case 1.