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.

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Presentation transcript:

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 = 2m and y = 2m for some integer m. 2.Then x = 2m and y = 2n for some integers m and n. 3.Then xy is even. 4.Case 1.