Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

lgbasallote

  • 2 years ago

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."

  • This Question is Closed
  1. joemath314159
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So we dont have to worry about negative numbers.

  2. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how does that relate?

  3. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    by p im referring to p and q by the way something like \(p \rightarrow q\)

  4. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What p?

  5. farmdawgnation
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The p is the conditional.

  6. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    p succeeds the "if" right?

  7. farmdawgnation
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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.

  8. farmdawgnation
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That'd be a problem.

  9. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    "only if" works like "if" in reverse.

  10. joemath314159
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  11. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ...i didn't know that....

  12. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    are there any other phrases that work as if in reverse?

  13. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    A if B becomes B only if A

  14. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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 \(A\rightarrow B\)

  15. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ahh just what i needed. what about necessary but not sufficient?

  16. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    necessary but not sufficient basically is the same as necessary.

  17. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    necessary and sufficient is bi-conditional.

  18. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The best thing to do is use 'rain' and 'clouds' and see if it makes sense. Then remember that rain implies clouds.

  19. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[(B \rightarrow A) \wedge (\neg A \rightarrow B)\] like that?

  20. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but clouds don't imply rain.

  21. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No, not like that.

  22. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because i remember something that said necessary but not sufficient and had this solution \[(q \rightarrow (\neg r \wedge \neg p)) \wedge \neg((\neg r \wedge \neg p) \rightarrow q)\]

  23. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  24. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I mean you could perhaps say \((B\rightarrow A) \wedge \neg (A\rightarrow B)\)

  25. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  26. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so any explanations for that?

  27. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well if \(B\rightarrow A\) means necessary and \(A\rightarrow B\) means sufficient then necessary but not sufficient could be written as \(B\rightarrow A)\wedge \neg (A\rightarrow B\))

  28. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ahh yes. makes sense

  29. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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.

  30. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's why i hate math.....

  31. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.