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Lime
 3 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?
Lime
 3 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?

This Question is Closed

Armor
 3 years ago
Best ResponseYou've already chosen the best response.0You 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.

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.464 = 4^3 and 64 = 8 ^2

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.4Hence 64 is a counter example to prove the statement wrong

Lime
 3 years ago
Best ResponseYou've already chosen the best response.0I have to prove the sentence false by giving the correct answer? Isn't that a counterpositive?

Lime
 3 years ago
Best ResponseYou've already chosen the best response.0Excuse me, *contrapositive.

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.4yes 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

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.4Lime .. "read" the question again.. You might have misunderstood the question..

Lime
 3 years ago
Best ResponseYou've already chosen the best response.0Well explained, thank you. :)

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.4You 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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