Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

princesspixie

  • 2 years ago

Write the contrapositive of the conditional statement below. “ n is a prime number implies that n=2 or n is an odd number.” Your answer must contain a conjunction in its premise.

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

    So in general, the contrapositive of the statement (\(\,p\implies q\)) is \((\neg \,q\implies \neg \,p\)). In this case, both your p and q are other sentences. Can you tell me what the "p" is in your conditional statement?

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

    n is a prime number

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

    Right. And the "q"?

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

    n is an odd number

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

    Almost. The "q" in your statement is "n=2 or n is an odd number." Notice that there's an "or" in this statement, so even this can be broken down into something like "q OR r," where q is "n=2", and r is "n is an odd number."

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

    oh i

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

    SEE

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

    So the statement "n is a prime number implies that n=2 or n is an odd number" can be rewritten as \[p\implies (q \vee r)\]

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

    if n is not a odd number then n is not a prime number or n = 2

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

    You're very close, and certainly have the right idea. The contrapositive of \(p\implies (q\vee r)\) is \(\neg(q\vee r)\implies \neg p\). Can you tell me what \(\neg(q\vee r)\) can be rewritten as?

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

    not sure

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

    This is a thing called "De Morgan's Law." It says that \[\neg(q\vee r) \Longleftrightarrow (\neg \,q) \wedge(\neg\,r) \]Can you translate this back into our statements?

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

    im confused

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

    So if q is "n=2," what is ~q?

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

    not =2

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

    |dw:1355893931180:dw|

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

    Right. And if r is "n is an odd number," what is ~r?

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

    n is not an odd number

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

    Bingo. So if we then combine those two statements, ~q AND ~r can be written as "n is not 2, and n is not an odd number." Make sense?

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

    yes

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

    Great. Then the contrapositive of your original statement should be "If n is not 2, and n is not an odd number, then n is not prime."

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

    that the answer it was that simple?

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

    That was it. Did it all make sense?

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

    You almost had it the first time, you just got a little mixed up with the second half of the statement.

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

    yes but what does it mean by Your answer must contain a conjunction in its premise.

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

    That just means that it has to have "and" somewhere in the statement. So the way it's written, it's fine. If we had written it as "If n is an even integer greater than two, then n is not prime" instead, which says the same thing, it would not be the correct solution because it does not contain "and."

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

    oh i see thanks so much!!

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

    You're welcome.

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

    • Attachments:

Ask your own question

Ask a Question
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.