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princesspixie

please tell me if this is correct: “All mathematicians must be good logicians and all good logicians must justify their claims.”

  • one year ago
  • one year ago

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  1. princesspixie
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    a) Write this statement symbolically as a conjunction of two conditional statements. Use three components (p, q, and r) and explicitly state what these are in your work. Remember: a component in logic is a simple declarative sentence that is either true or false. For example, "You are a student in MAT 101" would be a component statement. Note how this sentence contains no logical connectives like "not", "or", "and", etc. b) Write the negation of this statement symbolically. Explain your reasoning here. c) Now use part b) to write the negation of this statement verbally. A- p means 'person is mathematician' q means 'person is good logician' and r means 'justifies their claims' (p⟹q)∧(q⟹r) B- (~p⟹~q)∧(~q⟹~r) You put the ~ mark because that negates the statement. C - If a person is not a mathematician then the person is not a good logician or they do not justify their claims

    • one year ago
  2. princesspixie
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    The Boxes are arrows

    • one year ago
  3. satellite73
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    p: a person is a good mathematician q: a person is a good logician \(p\implies q\) : if a person is a good mathematician, then a person is a good logician rather tortured english, would probably say if a person is a good mathematician then he or she is also a good logician

    • one year ago
  4. princesspixie
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    what would the r statement be?

    • one year ago
  5. satellite73
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    \(q\implies r\) : if a person is a good logician, then they justify their claims

    • one year ago
  6. princesspixie
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    would i say r: person justifies their claims

    • one year ago
  7. satellite73
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    \[(p\implies q)\land (q\implies r)\] take those two statements and stick the word "and" between them

    • one year ago
  8. princesspixie
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    what do you mean those two statements and stick an and?

    • one year ago
  9. princesspixie
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    ^ is the symbol for and?

    • one year ago
  10. satellite73
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    yes

    • one year ago
  11. princesspixie
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    ok is the negation correct?

    • one year ago
  12. satellite73
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    if a person is a good logician, then they justify their claims and if a person is a good logician, then they justify their claims

    • one year ago
  13. princesspixie
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    thats the negation ?

    • one year ago
  14. satellite73
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    no that is \[(p\implies q)\land (q\implies r)\]

    • one year ago
  15. princesspixie
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    ok would I see.. would I put a ~ before the q and the r to negate it ?

    • one year ago
  16. princesspixie
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    or infront of all the letters?

    • one year ago
  17. satellite73
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    no you have to put \(\lnot\) in front of the whole thing

    • one year ago
  18. princesspixie
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    ¬(p⟹q)∧(q⟹r) ?

    • one year ago
  19. princesspixie
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    what is the explanation for that ?

    • one year ago
  20. satellite73
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    \[\lnot\left((p\implies q)\land (q\implies r)\right)\] then you should rewrite without the \(\implies \) and use demorgan laws

    • one year ago
  21. princesspixie
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    I dont understand..

    • one year ago
  22. satellite73
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    it will take a while do you know that \(p\implies q\equiv \lnot p\lor q\)?

    • one year ago
  23. princesspixie
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    No..

    • one year ago
  24. satellite73
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    to negate a statement you put a big \(\lnot\) in front of the whole thing, you do not negate each piece separately

    • one year ago
  25. princesspixie
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    ok how do I explain the reasoning for it?

    • one year ago
  26. satellite73
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    you have some statement "blah blah blah" the the negation is "it is not true that blah blah blah"

    • one year ago
  27. satellite73
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    if you want to negate it you have to rewrite it as \[(\lnot p \lor q)\land (\lnot q\lor r)\] then negate it as \[\lnot \left((\lnot p \lor q)\land (\lnot q\lor r)\right)\]

    • one year ago
  28. princesspixie
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    so both should be included in the answer?

    • one year ago
  29. satellite73
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    yes but we have more work to do

    • one year ago
  30. princesspixie
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    Im still not sure how I should explain the answer ..

    • one year ago
  31. satellite73
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    unless you are unfamiliar with these laws. perhaps you are supposed to do something else

    • one year ago
  32. satellite73
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    your original statement All mathematicians must be good logicians and all good logicians must justify their claims is correct

    • one year ago
  33. princesspixie
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    ive never seen that little hook thing, but i see that in the textbook it says converse inverse and contrapostive .. not sure if that helps

    • one year ago
  34. satellite73
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    actually i would get rid of the word "must"

    • one year ago
  35. satellite73
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    "all mathematicians are good logicians and all good logicians justify their claims" perhaps is better

    • one year ago
  36. princesspixie
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    thats why i thought this symbol would be in the equation ~

    • one year ago
  37. satellite73
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    \(\lnot\) is the same as ~

    • one year ago
  38. satellite73
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    means "not"

    • one year ago
  39. princesspixie
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    ok so should i use the ~ if that what the text book uses?

    • one year ago
  40. princesspixie
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    ok .. how should i explain that in simple terms?

    • one year ago
  41. princesspixie
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    is this good... The symbol ~ means not. Therefore, if a person is not a good mathematician then the person is not a good logician, and the person cannot justify their claims.

    • one year ago
  42. satellite73
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    i would think perhaps the negation, without using the symbols, would be not all mathematicians are good logicians or not all logicians justify their claims

    • one year ago
  43. princesspixie
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    ok so i should use that instead of if a person is not a good... ?

    • one year ago
  44. satellite73
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    if a person is a good mathematician, then they are a good logician the statement if a person is not a good mathematician then the person is not a good logician is not the negation, it is the "inverse"

    • one year ago
  45. princesspixie
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    ok I understand

    • one year ago
  46. princesspixie
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    so would that be a good explanation?

    • one year ago
  47. satellite73
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    then negation of "if a person is a good mathematician, then they are a good logician" is there is some mathematician who is not a good logician

    • one year ago
  48. princesspixie
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    thats the answer for C?

    • one year ago
  49. satellite73
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    i forget what C is

    • one year ago
  50. princesspixie
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    c) Now use part b) to write the negation of this statement verbally.

    • one year ago
  51. satellite73
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    the negation of the whole thing would read something like "there is a good mathematician who is not a good logician, or there is a good logician who does not justify their claims

    • one year ago
  52. satellite73
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    the negation of the "and" statement is one or the other is false

    • one year ago
  53. satellite73
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    really to do this symbolically takes a while

    • one year ago
  54. princesspixie
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    ok I see

    • one year ago
  55. satellite73
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    \[\lnot \left((\lnot p \lor q)\land (\lnot q\lor r)\right)\] \[\lnot(\lnot p\lor q)\lor \lnot(\lnot q \lor r)\] \[(p\land \lnot q)\lor (q\land \lnot r)\]

    • one year ago
  56. satellite73
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    the last statement says there is a good mathematician who is not a good logician or there is a good logician who does not justify their claims

    • one year ago
  57. princesspixie
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    oh i see ok thanks!!

    • one year ago
  58. satellite73
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    yw good luck with this

    • one year ago
  59. princesspixie
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    thanks so much for all your help!!

    • one year ago
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