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lgbasallote

Logic Question: A positive integer is prime only if it has no other divisors other than 1 and itself. Why is the p here "A positive integer is prime" and not "it has no other divisors other than 1 and itself."

  • one year ago
  • one year ago

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  1. joemath314159
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    So we dont have to worry about negative numbers.

    • one year ago
  2. lgbasallote
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    how does that relate?

    • one year ago
  3. lgbasallote
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    by p im referring to p and q by the way something like \(p \rightarrow q\)

    • one year ago
  4. wio
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    What p?

    • one year ago
  5. farmdawgnation
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    The p is the conditional.

    • one year ago
  6. lgbasallote
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    p succeeds the "if" right?

    • one year ago
  7. farmdawgnation
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    So you'd rewrite this as, If positive integer n is prime, it has no other divisors other than 1 and itself. However, you CAN'T say.. If n has no other divisors than 1 and itself, it is a positive integer.

    • one year ago
  8. farmdawgnation
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    That'd be a problem.

    • one year ago
  9. wio
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    "only if" works like "if" in reverse.

    • one year ago
  10. joemath314159
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    ah, i misunderstood. I would read that statement as: If a number has no divisors other than one and itself, then it is prime.

    • one year ago
  11. lgbasallote
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    ...i didn't know that....

    • one year ago
  12. lgbasallote
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    are there any other phrases that work as if in reverse?

    • one year ago
  13. wio
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    A if B becomes B only if A

    • one year ago
  14. wio
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    A is necessary for B means \(B\rightarrow A\). A is sufficient for B means \(A\rightarrow B\). A if B means \(B\rightarrow A\) A only if B means \(A\rightarrow B\)

    • one year ago
  15. lgbasallote
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    ahh just what i needed. what about necessary but not sufficient?

    • one year ago
  16. wio
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    necessary but not sufficient basically is the same as necessary.

    • one year ago
  17. wio
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    necessary and sufficient is bi-conditional.

    • one year ago
  18. wio
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    The best thing to do is use 'rain' and 'clouds' and see if it makes sense. Then remember that rain implies clouds.

    • one year ago
  19. lgbasallote
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    \[(B \rightarrow A) \wedge (\neg A \rightarrow B)\] like that?

    • one year ago
  20. wio
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    but clouds don't imply rain.

    • one year ago
  21. wio
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    No, not like that.

    • one year ago
  22. lgbasallote
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    because i remember something that said necessary but not sufficient and had this solution \[(q \rightarrow (\neg r \wedge \neg p)) \wedge \neg((\neg r \wedge \neg p) \rightarrow q)\]

    • one year ago
  23. lgbasallote
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    the statement was this: For hiking to be safe, it is necessary but not sufficient that berries be not ripe along the trail and for grizzly bears not to have been seen in the area

    • one year ago
  24. wio
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    I mean you could perhaps say \((B\rightarrow A) \wedge \neg (A\rightarrow B)\)

    • one year ago
  25. lgbasallote
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    the p, q, r are these: p: Grizzly bears have been sean in the area q: hiking is safe r: berries are ripe along the trail

    • one year ago
  26. lgbasallote
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    so any explanations for that?

    • one year ago
  27. wio
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    Well if \(B\rightarrow A\) means necessary and \(A\rightarrow B\) means sufficient then necessary but not sufficient could be written as \(B\rightarrow A)\wedge \neg (A\rightarrow B\))

    • one year ago
  28. lgbasallote
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    ahh yes. makes sense

    • one year ago
  29. wio
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    But there is a big of an ambiguity for me, because when they say necessary and not sufficient, do they mean necessary but not necessarily sufficient, or necessary and never sufficient.

    • one year ago
  30. lgbasallote
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    that's why i hate math.....

    • one year ago
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