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


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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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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 first line of the proof if a divides b then a divides b c

  • 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.


What is the first line of the proof if a divides b then a divides b c

  • 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 = …


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?

  • 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.


What is the first line of the proof if a divides b then a divides b c

  • 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.


What is the first line of the proof if a divides b then a divides b c

  • 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.


What is the first line of the proof if a divides b then a divides b c

  • 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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