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hali12

  • 2 years ago

Let p and q represent the statements: p: Jose is running track. q: Jose is not winning the race. Express the following statement symbolically: Jose is winning the race..... a) p.. b) q.. c)~q.. d) ~p

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  1. hali12
    • 2 years ago
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    @jim_thompson5910 is this the same as the last ones?

  2. jim_thompson5910
    • 2 years ago
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    q: Jose is not winning the race.

  3. jim_thompson5910
    • 2 years ago
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    ~q is the opposite of q

  4. jim_thompson5910
    • 2 years ago
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    So if q says one thing then ~q (NOT q) says the complete opposite thing q says

  5. jim_thompson5910
    • 2 years ago
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    so ~q is like saying Jose is NOT not winning the race ...a bit confusing, but the two "not"s cancel giving us ~q: Jose is winning the race

  6. hali12
    • 2 years ago
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    so then its p?

  7. jim_thompson5910
    • 2 years ago
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    p is the statement Jose is running track

  8. jim_thompson5910
    • 2 years ago
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    agreed?

  9. hali12
    • 2 years ago
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    yea

  10. jim_thompson5910
    • 2 years ago
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    does that have anything to do with "Jose is winning the race" ?

  11. hali12
    • 2 years ago
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    not really

  12. jim_thompson5910
    • 2 years ago
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    so "Jose is winning the race" doesn't involve p at all

  13. jim_thompson5910
    • 2 years ago
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    reread what I wrote at the beginning of this thread

  14. jim_thompson5910
    • 2 years ago
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    and hopefully something will click

  15. hali12
    • 2 years ago
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    q?

  16. jim_thompson5910
    • 2 years ago
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    closer, but still no

  17. hali12
    • 2 years ago
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    ~q

  18. jim_thompson5910
    • 2 years ago
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    you got it

  19. jim_thompson5910
    • 2 years ago
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    look above to see why

  20. jim_thompson5910
    • 2 years ago
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    I wrote it out at the top

  21. hali12
    • 2 years ago
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    ohh i didnt even relize it, wow.... thank you so much, i also have 2 more, i have one that i really dont know

  22. jim_thompson5910
    • 2 years ago
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    its ok, i was wondering about that lol

  23. hali12
    • 2 years ago
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    Look at the argument below. Which of the following symbolic statements shows the set-up used to find the validity of the argument? If Mario studies hard, then he gets good grades. Mario got good grades. Therefore, Mario studied hard. p: Mario studies hard. q: Mario gets good grades

  24. jim_thompson5910
    • 2 years ago
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    First off, is that argument valid?

  25. jim_thompson5910
    • 2 years ago
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    oh wait, nvm they're asking a different question

  26. hali12
    • 2 years ago
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    a.) [(p → q) ∧ ~q] .'.p b.)[(p → q) → q] ∴ p c.)[(p → q) ∧ q] ∴ q d.) [(p → q) ∧ q] ∴ p

  27. jim_thompson5910
    • 2 years ago
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    hmm interesting way to put it

  28. jim_thompson5910
    • 2 years ago
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    "If Mario studies hard, then he gets good grades." translates to ...???

  29. hali12
    • 2 years ago
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    p?

  30. jim_thompson5910
    • 2 years ago
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    p is just "Mario studies hard"

  31. jim_thompson5910
    • 2 years ago
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    how do we incorporate the "he gets good grades" part?

  32. hali12
    • 2 years ago
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    p -> q

  33. jim_thompson5910
    • 2 years ago
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    good

  34. jim_thompson5910
    • 2 years ago
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    "If Mario studies hard, then he gets good grades." translates to p -> q

  35. jim_thompson5910
    • 2 years ago
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    now tack on the statement "Mario got good grades" So what does "If Mario studies hard, then he gets good grades. Mario got good grades. " translate to ???

  36. hali12
    • 2 years ago
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    [(p → q) ∧ ~q] .'. p

  37. jim_thompson5910
    • 2 years ago
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    not quite

  38. jim_thompson5910
    • 2 years ago
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    ~q means he did NOT get good grades, but it clearly says he did

  39. hali12
    • 2 years ago
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    [(p → q) ∧ ~q] .'. p

  40. hali12
    • 2 years ago
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    [(p->q) ^q] .'. p

  41. jim_thompson5910
    • 2 years ago
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    better

  42. hali12
    • 2 years ago
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    so is that it then?

  43. jim_thompson5910
    • 2 years ago
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    yes it is

  44. hali12
    • 2 years ago
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    oh ok, thanks, and this will be the last one i promise,: Which of the following is the equivalent of the inverse statement? a.) the negation of the statement.. b.) the converse of the statement.... c.)the contrapositive of the statement... d.)the conditional statement

  45. jim_thompson5910
    • 2 years ago
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    In general Original = contrapositive and inverse = converse

  46. jim_thompson5910
    • 2 years ago
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    So it's b)

  47. jim_thompson5910
    • 2 years ago
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    the inverse of p -> q is ~p -> ~q -------------- that's equivalent to ~~q -> ~~p which is the same as q -> p but this is the converse So this shows that the inverse and the converse represent the same thing

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