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What is the first line of the proof? If a divides b, then a divides b – c.

What is the first line of the proof? If a divides b, then a divides b – c. If a divides b, then a divides c. Assume a divides b – c. Assume a divides b and a divides c. Assume a does not divide b and a does not divide c. What is the next line of the proof? Then a must divide b – c.

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What is the first line of the proof? If a divides b, then a divides b – c.

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

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

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

  4. What is the first line of the proof? • Assume a divides c. • Assume c divides a. • Assume a divides b and b divides c. • Assume b divides a and c divides b. • Assume a does not divide b and b does not divide c. • Assume a does not divide b or b does not divide c.

  5. What is the next line of the proof? • Assume xy is odd. • Assume xy is even. • Assume x and y are both odd. • Assume x and y are both even. • Assume x or y is odd. • Assume x or y is even.

  6. What is the next line of the proof? • Assume xy is odd. • Assume xy is even. • Assume x and y are both odd. • Assume x and y are both even. • Assume x or y is odd. • Assume x or y is even.

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

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