Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Lime

Raise your hand if you love Inductive Reasoning! I've wrapped my mind around this one. Choose a counterexample that proves that the conjecture below is false. "Other than the number 1, there are no numbers less than 100 that are both perfect squares and perfect cubes." You have a choice of 36, 64, 16, and 8. So, I have to prove this statement false by providing a number that IS a perfect square. I've come to the conclusion that the answer is 16. Or is this a trick question? 8 is not a perfect square and therefore proves the sentence true?

  • one year ago
  • one year ago

  • This Question is Closed
  1. mathslover
    Best Response
    You've already chosen the best response.
    Medals 3

    64?

    • one year ago
  2. Armor
    Best Response
    You've already chosen the best response.
    Medals 0

    You need to find a number that is both a perfect square and a perfect cube. 16 is not a perfect cube, so it isn't a counter example.

    • one year ago
  3. mathslover
    Best Response
    You've already chosen the best response.
    Medals 3

    64 = 4^3 and 64 = 8 ^2

    • one year ago
  4. mathslover
    Best Response
    You've already chosen the best response.
    Medals 3

    Hence 64 is a counter example to prove the statement wrong

    • one year ago
  5. Lime
    Best Response
    You've already chosen the best response.
    Medals 0

    I have to prove the sentence false by giving the correct answer? Isn't that a counter-positive?

    • one year ago
  6. Lime
    Best Response
    You've already chosen the best response.
    Medals 0

    Excuse me, *contra-positive.

    • one year ago
  7. mathslover
    Best Response
    You've already chosen the best response.
    Medals 3

    yes that proves that the sentence if false... the statement says that there is only one number i.e. 1 which is both perfect square and perfect cube You have to find a number other than "1" which is both perfect square and perfect cube.. i.e. 64 .. which proves the above statement wrong

    • one year ago
  8. mathslover
    Best Response
    You've already chosen the best response.
    Medals 3

    Lime .. "read" the question again.. You might have misunderstood the question..

    • one year ago
  9. Lime
    Best Response
    You've already chosen the best response.
    Medals 0

    Well explained, thank you. :)

    • one year ago
  10. mathslover
    Best Response
    You've already chosen the best response.
    Medals 3

    You r welcome Lime.. Also ... best of luck for your further questions.. You must try to understand these type of questions by reading again and again

    • one year ago
    • Attachments:

See more questions >>>

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.