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Lime

  • 2 years ago

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?

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  1. mathslover
    • 2 years ago
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    64?

  2. Armor
    • 2 years ago
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    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.

  3. mathslover
    • 2 years ago
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    64 = 4^3 and 64 = 8 ^2

  4. mathslover
    • 2 years ago
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    Hence 64 is a counter example to prove the statement wrong

  5. Lime
    • 2 years ago
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    I have to prove the sentence false by giving the correct answer? Isn't that a counter-positive?

  6. Lime
    • 2 years ago
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    Excuse me, *contra-positive.

  7. mathslover
    • 2 years ago
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    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

  8. mathslover
    • 2 years ago
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    Lime .. "read" the question again.. You might have misunderstood the question..

  9. Lime
    • 2 years ago
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    Well explained, thank you. :)

  10. mathslover
    • 2 years ago
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    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

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