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Deductive Reasoning

kendra avatar
kendra
21 diapositives · 348 Views · Oct 15, 2014

Dive deep into the world of logic and deduction with this engaging guide to mastering deductive reasoning. Learn how to identify hypotheses, conclusions, and counterexamples while honing your problem-solving skills. The perfect resource for enhancing your logical thinking abilities.

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Deductive Reasoning
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  1. “The proof is in the pudding.” “Indubitably.” Le pompt de pompt le solve de crime!" Je solve le crime. Pompt de pompt pompt." Deductive Reasoning 2-1 Written Ex. P 35.

  2. 2-1 Written Ex. P 34. Underline the hypothesis and box the conclusion. 1. If 3x – 7 = 32, then x = 13. 2. I can’t sleep if I am tired. 3. I’ll try if you will.

  3. Underline the hypothesis and box the conclusion. 4. If , then is a right angle. 5. a + b = a implies b = 0. 6. x = - 5 only if x2 = 25.

  4. Rewrite each pair of conditionals as a biconditional. • If B is between A and C, then AB + BC = AC. • If AB + BC = AC, then B is between A and C. B is between A and C if and only if AB + BC = AC • If , then is a straight angle. • If is a straight angle, then . if and only if is a straight angle.

  5. Write each biconditional as a pair of conditionals. 9. Points are collinear if and only if they all lie in one line. If points are collinear, then they all lie in one line. If all points lie in one line, then they are collinear. 10. Points lie in on plane if and only if they are coplanar. If points lie in on plane, then they are coplanar. If points are coplanar, then they lie in on plane.

  6. Provide a counter example to show that each statement is false. When trying these algebraic us negative numbers , 1, 0, 1, 10, and fractions between 0 and 1 as test values. Let a = 1 and b = -1 (-1)(1) < 0 and a > 0 11. If ab < 0 , then a < 0. n = 0 n2 = 5n but n is not = 5 12. If n2 = 5n , then n = 5. 13. If point G is on , then G is on . A B G

  7. Provide a counter example to show that each statement is false. Let x = - 1 and y = -1 (-1)(-1) > 5(-1) 1 > -5 But – 1 is not > 5 14. If xy > 5y , then x > 5. 15. If a four-sided figure has 4 right angles, then it has four congruent sides. A rectangle. 15. If a four-sided figure has four congruent sides, then it has 4 right angles. Diamond or rhombus.

  8. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. True 17. If x = - 6, then . If , then x = - 6. False x could = + 6

  9. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. 18. If , then x = - 2 . False x could = + 2 Quadratic equations have 2 roots. 18. If x = - 2 , then . True

  10. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. True 19. If b > 4 , then 5b > 20. If 5b > 20, then b > 4. True

  11. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. 20. If , then is not obtuse. True If is not obtuse, then . False T could = 90, 80, ..

  12. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. 21. If Pam lives in Chicago, then she lives in Illinois. True If Pam lives in Illinois, then she lives in Chicago. False, there are a lot of other cities in Illinois.

  13. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. 22. If , then . True If , then . True: all definitions are reversible.

  14. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. 23. if . True 23. If , then . False a could be -10.

  15. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. Note “only if” is not the same as “if”. Only if means “then” 24. x = 1 only if . True If then x = 1 . False x could be 0.

  16. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. Note “only if” is not the same as “if”. Only if means “then” 25. n > 5 only if n > 7 . False n could be 6. If n > 7 , then n > 5. True

  17. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. 26. ab = 0 implies that a = 0 or b = 0. True a = 0 or b = 0 implies that ab = 0. True

  18. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. False 27. If points D, E, and F are collinear, then DE + EF = DF. Counterexample E F E D If DE + EF = DF, then points D, E, and F are collinear. False Counterexample D F

  19. Tell whether each statement is true or false. Then write the converse and tell whether the converse is true of false. 28. P is the midpoint of implies that GH = 2 PG. True GH = 2 PG. implies that P is the midpoint of P 1 False G H 2 Counterexample

  20. 29. Write a definition of congruent angles as a biconditional. 30. Write a definition of a right angle as a biconditional. is a right angle if and only if

  21. C’est fini. Good day and good luck.