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math_proof

  • 2 years ago

what is the negation" all cabbages are green

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  1. nickhouraney
    • 2 years ago
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    be more specific

  2. math_proof
    • 2 years ago
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    suppose that "if z is a w-group then z is solvable" is a true statement, you also know that the "z is solvable" is true. can you deduce that "z is a w-group" is true?

  3. omgitsjc
    • 2 years ago
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    i wish i was good a math

  4. ChmE
    • 2 years ago
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    no because for the statement to be true z is a w-group could be true or false

  5. lgbasallote
    • 2 years ago
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    unless there's more to that question...don't you just put a "not" before the adjective?

  6. math_proof
    • 2 years ago
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    igbasallote what are you talking about?

  7. ChmE
    • 2 years ago
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    in a "if p then q" statement. if "if p" is false the whole statement is true regardless of then p. If they are both true then it is also true. It can only be false if "if p" is true and "then q" is flase.

  8. ChmE
    • 2 years ago
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    I can give you an example to clarify if you want

  9. ChmE
    • 2 years ago
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    I was answering ur second question by the way

  10. ChmE
    • 2 years ago
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    @lgbasollote was answering your first.

  11. ChmE
    • 2 years ago
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    and @lgbasallote you were correct

  12. math_proof
    • 2 years ago
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    I don't get what lgbasallote was saying

  13. ChmE
    • 2 years ago
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    actually let me look at me logic notes to make sure.

  14. ChmE
    • 2 years ago
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    The correct answer to your first question is All cabages are not green

  15. ChmE
    • 2 years ago
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    Like the car is red. The negation is the car is not red

  16. math_proof
    • 2 years ago
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    why isn't it not all cabbages are green

  17. ChmE
    • 2 years ago
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    because that implies that some are green

  18. ChmE
    • 2 years ago
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    we want to to do a complete opposite

  19. ChmE
    • 2 years ago
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    its confusing I know

  20. math_proof
    • 2 years ago
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    so u wan't to tell that none of them are green right?

  21. ChmE
    • 2 years ago
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    correct

  22. ChmE
    • 2 years ago
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    Did you understand what I was saying to your second question

  23. math_proof
    • 2 years ago
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    im trying to figure it out now

  24. ChmE
    • 2 years ago
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    What class is this? just curious

  25. math_proof
    • 2 years ago
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    advanced mathematics

  26. math_proof
    • 2 years ago
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    whole class based on proofs basically

  27. math_proof
    • 2 years ago
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    induction proofing, contradictions, and now we are at sets theories

  28. ChmE
    • 2 years ago
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    I took a class called mathematical logic which involved a bunch of this stuff. Kinda interesting kinda hell

  29. ChmE
    • 2 years ago
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    I hate sets

  30. ChmE
    • 2 years ago
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    Only class I have ever had to drop cuz i was failing. Sets, relations, and functions.

  31. ChmE
    • 2 years ago
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    Let me know if you don't understand my explanation about your second question I can provide an example that would make it clearer. I'm going to move on to other questions

  32. math_proof
    • 2 years ago
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    thats pretty much what i am in now, and let me tell you that I have no idea how im going to pass that class

  33. ChmE
    • 2 years ago
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    Logic was kinda fun. Sets is hell. I would master definitions. completely understand what a subset is and what real numbers and complex numbers. just master definitions because you can use those in ur proofs. I wish I had done that.

  34. math_proof
    • 2 years ago
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    im trying to figure out that example and don't completely get it So P=>Q so if z is a w-group then z is solvable IS TRUE, then "Z is solvable is also true" why s s "Z is a w-group false?

  35. DanielxAK
    • 2 years ago
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    The negation of "all cabbages are green" is "there exists a cabbage which is not green". All is a quantifier.

  36. math_proof
    • 2 years ago
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    isn't the negation "all cabbages are not green?"

  37. ChmE
    • 2 years ago
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    So @DanielxAK we just had to show that for all to be false one is true?

  38. ChmE
    • 2 years ago
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    lets use p and q for your question all the words are confusing me lol. So the question is essentially... If, if p then q is true, then q is true" So its a nested statement?

  39. ChmE
    • 2 years ago
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    P-->Q T Premise Q T Prove

  40. DanielxAK
    • 2 years ago
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    I'm not sure I understand what you mean by that. If it was phrased, cabbage is green. Then, the negation would be cabbage is not green. But, you have "all cabbages are green". So, the negation would be "there exists a cabbage which isn't green". The negation of all is one. This might be able to explain it better than I can: http://www.math.cornell.edu/~hubbard/negation.pdf

  41. ChmE
    • 2 years ago
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    Good catch Daniels

  42. ChmE
    • 2 years ago
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    Your second question @math_proof, I think it is a correct statement. Because "if p" is true, for the statement to be true (which it is by a premise) "then q" must be true. and "if p" is false. Then "then q" is assumed true because it can't be proven otherwise.

  43. ChmE
    • 2 years ago
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    You got me inerested now. I dug out my logic notes. Law of Equivalence for Implication and Disjunction (LEID) states IF p-->q is true, THEN not p or q is true

  44. math_proof
    • 2 years ago
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    still confused omg

  45. ChmE
    • 2 years ago
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    So we are Given that P --> Q is true correct? and we have to prove that Q is true? am I understanding right?

  46. math_proof
    • 2 years ago
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    we know that Q is true

  47. math_proof
    • 2 years ago
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    so P can be either true of false

  48. math_proof
    • 2 years ago
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    so P=>Q, z is a w-group then z is solvable" is a true statement, so P->Q is true and we know Q is true because "Z is solvable" so P can be either True of False? thats what i'm thinking

  49. ChmE
    • 2 years ago
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    P->Q T Premise Q T Premise P T Prove Ok I'm on the right page

  50. ChmE
    • 2 years ago
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    So I would say the answer is ~P V P

  51. math_proof
    • 2 years ago
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    thats based on truth table on logical implication

  52. ChmE
    • 2 years ago
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    I agree

  53. math_proof
    • 2 years ago
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    so we can't deduce if P is true

  54. ChmE
    • 2 years ago
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    I have this cheat sheet that my teacher made us with all the laws of logic that can be used in a proof. If you'd like it i'll email it to you. Just private message me your email. If you are not comfortable with that I guess I could post it on this thread, but I've got warned for stuff like that

  55. ChmE
    • 2 years ago
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    I guess we can't for certain

  56. math_proof
    • 2 years ago
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    omg thanks so much for that, I actually get it now

  57. ChmE
    • 2 years ago
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    No problem. When you jump into sets I will be no help. Like I said earlier for sets proofs I would master definitions because my teacher used a lot of "By def'n..." in her proofs

  58. math_proof
    • 2 years ago
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    i never heard of this website, but now that i discovered it is so useful and helpful and for free

  59. math_proof
    • 2 years ago
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    how do you give a medal?

  60. math_proof
    • 2 years ago
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    oo oki got it

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