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Indirect Reasoning

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Indirect Reasoning

  1. 1. Reasoning
  2. 2. How do you know this car was built after the year 1990? Reasoning If the car was built before the 90's it would not have an mp3 player in it. It does have an mp3 player in it so it must be built after the year 1990.
  3. 3. 1. Examine the conclusion you must prove 2. Assume the opposite of what you are proving 3. Use logical reasoning to develop a statement that is contradictory to your assumption. I dr c R a o i g n ie t e s nn !
  4. 4. How do you know this car was built before the year 1990? Reasoning If the car was built before the 90's it would not have an mp3 player in it. It does have an mp3 player in it so it must be built after the year 1990. 1. Examine the conclusion you must prove Built after 1990 2. Assume the opposite of what you are proving Built before 1990 3. Use logical reasoning to develop a statement that is contradictory to your assumption. Need reasoning to contradict the statement built before 1990 If the car was built before the 90's it would not have an mp3 player in it. It does have an mp3 player in it so it must be built after the year 1990.
  5. 5. A Given: ABC AB = AC angle BAD = angle CAD then BD = CD C B D 1. Examine the conclusion you must prove Prove BD ≠ CD 2. Assume the opposite of what you are proving Assume BD = CD 3. Use logical reasoning to develop a statement that is contradictory to your assumption. Assume BD = CD We are told AB = AC it follows that AB = AC = CD and ΔBAD = ΔCAD therefore angle BAD = angle CAD But we are told angle BAD ≠ angle CAD Therefore, we know that our assumption that BD = CD is false and we have proven that... BC ≠ CD
  6. 6. Prove that √3 is irrational assume that √3 is rational √3 = a b (√3)b = a 2 2 3b = a The number of factors of 3 in a squared integer is either none or an even number. 2 example 6 = 3*3*4 2 example 5 = no factors of 3 2 example 9 = 81 = 3*3*3*3 2 2 On the left side of 3b = a there must be an odd number of factors because of the extra multiple of 3 While on the right side there is an even number. 2 2 so we know that 3b ≠a which was necessarily true if √3 is rational therefore √3 is irrational
  7. 7. Direct Reasoning - use what you know to prove something A B O 0 104 C

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