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princesspixie Group Title

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

  • 2 years ago
  • 2 years ago

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  1. princesspixie Group Title
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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

    • 2 years ago
  2. princesspixie Group Title
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    The Boxes are arrows

    • 2 years ago
  3. satellite73 Group Title
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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

    • 2 years ago
  4. princesspixie Group Title
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    what would the r statement be?

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

    • 2 years ago
  6. princesspixie Group Title
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    would i say r: person justifies their claims

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

    • 2 years ago
  8. princesspixie Group Title
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    what do you mean those two statements and stick an and?

    • 2 years ago
  9. princesspixie Group Title
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    ^ is the symbol for and?

    • 2 years ago
  10. satellite73 Group Title
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    yes

    • 2 years ago
  11. princesspixie Group Title
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    ok is the negation correct?

    • 2 years ago
  12. satellite73 Group Title
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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

    • 2 years ago
  13. princesspixie Group Title
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    thats the negation ?

    • 2 years ago
  14. satellite73 Group Title
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    no that is \[(p\implies q)\land (q\implies r)\]

    • 2 years ago
  15. princesspixie Group Title
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    ok would I see.. would I put a ~ before the q and the r to negate it ?

    • 2 years ago
  16. princesspixie Group Title
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    or infront of all the letters?

    • 2 years ago
  17. satellite73 Group Title
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    no you have to put \(\lnot\) in front of the whole thing

    • 2 years ago
  18. princesspixie Group Title
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    ¬(p⟹q)∧(q⟹r) ?

    • 2 years ago
  19. princesspixie Group Title
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    what is the explanation for that ?

    • 2 years ago
  20. satellite73 Group Title
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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

    • 2 years ago
  21. princesspixie Group Title
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    I dont understand..

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

    • 2 years ago
  23. princesspixie Group Title
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    No..

    • 2 years ago
  24. satellite73 Group Title
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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

    • 2 years ago
  25. princesspixie Group Title
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    ok how do I explain the reasoning for it?

    • 2 years ago
  26. satellite73 Group Title
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    you have some statement "blah blah blah" the the negation is "it is not true that blah blah blah"

    • 2 years ago
  27. satellite73 Group Title
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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 \[\lnot \left((\lnot p \lor q)\land (\lnot q\lor r)\right)\]

    • 2 years ago
  28. princesspixie Group Title
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    so both should be included in the answer?

    • 2 years ago
  29. satellite73 Group Title
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    yes but we have more work to do

    • 2 years ago
  30. princesspixie Group Title
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    Im still not sure how I should explain the answer ..

    • 2 years ago
  31. satellite73 Group Title
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    unless you are unfamiliar with these laws. perhaps you are supposed to do something else

    • 2 years ago
  32. satellite73 Group Title
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    your original statement All mathematicians must be good logicians and all good logicians must justify their claims is correct

    • 2 years ago
  33. princesspixie Group Title
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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

    • 2 years ago
  34. satellite73 Group Title
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    actually i would get rid of the word "must"

    • 2 years ago
  35. satellite73 Group Title
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    "all mathematicians are good logicians and all good logicians justify their claims" perhaps is better

    • 2 years ago
  36. princesspixie Group Title
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    thats why i thought this symbol would be in the equation ~

    • 2 years ago
  37. satellite73 Group Title
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    \(\lnot\) is the same as ~

    • 2 years ago
  38. satellite73 Group Title
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    means "not"

    • 2 years ago
  39. princesspixie Group Title
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    ok so should i use the ~ if that what the text book uses?

    • 2 years ago
  40. princesspixie Group Title
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    ok .. how should i explain that in simple terms?

    • 2 years ago
  41. princesspixie Group Title
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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.

    • 2 years ago
  42. satellite73 Group Title
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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

    • 2 years ago
  43. princesspixie Group Title
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    ok so i should use that instead of if a person is not a good... ?

    • 2 years ago
  44. satellite73 Group Title
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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"

    • 2 years ago
  45. princesspixie Group Title
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    ok I understand

    • 2 years ago
  46. princesspixie Group Title
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    so would that be a good explanation?

    • 2 years ago
  47. satellite73 Group Title
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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

    • 2 years ago
  48. princesspixie Group Title
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    thats the answer for C?

    • 2 years ago
  49. satellite73 Group Title
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    i forget what C is

    • 2 years ago
  50. princesspixie Group Title
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    c) Now use part b) to write the negation of this statement verbally.

    • 2 years ago
  51. satellite73 Group Title
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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

    • 2 years ago
  52. satellite73 Group Title
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    the negation of the "and" statement is one or the other is false

    • 2 years ago
  53. satellite73 Group Title
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    really to do this symbolically takes a while

    • 2 years ago
  54. princesspixie Group Title
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    ok I see

    • 2 years ago
  55. satellite73 Group Title
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    \[\lnot \left((\lnot p \lor q)\land (\lnot q\lor r)\right)\] \[\lnot(\lnot p\lor q)\lor \lnot(\lnot q \lor r)\] \[(p\land \lnot q)\lor (q\land \lnot r)\]

    • 2 years ago
  56. satellite73 Group Title
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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

    • 2 years ago
  57. princesspixie Group Title
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    oh i see ok thanks!!

    • 2 years ago
  58. satellite73 Group Title
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    yw good luck with this

    • 2 years ago
  59. princesspixie Group Title
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    thanks so much for all your help!!

    • 2 years ago
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