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LOGIC :

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LOGIC :

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  1. LOGIC: SYLLOGISMS

  2. Syllogism: A set of statements called premises, which lead to one logical conclusion.

  3. If the premises are true, (and we assume they are), then the conclusion must be true.

  4. (Note: This symbol means “Therefore”. It signals the conclusion.)

  5. Law of Syllogism

  6. If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other. __________________________

  7. If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other. __________________________

  8. If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other. __________________________

  9. If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, thenits diagonals bisect. __________________________ If a figure is a rectangle, then its diagonals bisect.

  10. Law of Detachment

  11. If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________

  12. If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________

  13. If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________ ABCD is a parallelogram.

  14. Law of Contrapositive

  15. If a figure is a rectangle, then it is a parallelogram. ABCD is not a parallelogram. __________________________

  16. If a figure is a rectangle, then it is a parallelogram. ABCD is not a parallelogram. __________________________

  17. If a figure is a rectangle, then it is a parallelogram. ABCD is not a parallelogram. __________________________ ABCD is not a rectangle.

  18. Time to Practice:

  19. In the following examples, use the given law of syllogism to draw the correct conclusion from the set of premises.

  20. 1. If frogs fly then toads talk. Frogs fly. -----------------------------

  21. Law of Detachment

  22. 1. If frogs fly then toads talk. Frogs fly. -----------------------------

  23. 1. If frogs fly then toads talk. Frogs fly. ----------------------------- Toads talk.

  24. 2. If hens heckle then crows don’t care. Crows care. -----------------------

  25. Law of Contrapositive

  26. 2. If hens heckle then crows don’t care. Crows care. -----------------------

  27. 2. If hens heckle then crows don’t care. Crows care. ----------------------- Hens don’t heckle.

  28. 3. If ants don’t ask then flies don’t fret. Ants don’t ask. ----------------------------

  29. Law of Detachment

  30. 3. If ants don’t ask then flies don’t fret. Ants don’t ask. ----------------------------

  31. 3. If ants don’t ask then flies don’t fret. Ants don’t ask. ---------------------------- Flies don’t fret.

  32. 4. If Dave dives then Cal caves. If Cal caves then Hank hikes. -------------------------------------

  33. Law of Syllogism

  34. 4. If Dave dives then Cal caves. If Cal caves then Hank hikes. -------------------------------------

  35. 4. If Dave dives then Cal caves. If Cal caves then Hank hikes. ------------------------------------- If Dave dives then Hank hikes.

  36. 5. If dogs duel then rats wrestle. Rats don’t wrestle. -----------------------------

  37. Law of Contrapositive

  38. 5. If dogs duel then rats wrestle. Rats don’t wrestle. -----------------------------

  39. 5. If dogs duel then rats wrestle. Rats don’t wrestle. ----------------------------- Dogs don’t duel.

  40. Why does this one work?

  41. Here are the premises:

  42. Replace with contrapositive:

  43. Replace with contrapositive:

  44. Use Law of Detatchment:

  45. Law of Contrapositive