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Problem. All As are B If I can do X, then I can find an A which is not a B Consider these two statements. Can they both be true at once? If so, how?. Problem. All G11 students at East are in white shirts

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Problem

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Problem

Problem

  • All As are B

  • If I can do X, then I can find an A which is not a B

    Consider these two statements. Can they both be true at once? If so, how?


Problem1

Problem

  • All G11 students at East are in white shirts

  • If I can take a picture of a G11 student who is in a blue shirt, then I have found a G11 student who is not wearing a white shirt


Problem2

Problem

  • All As are B

  • If I can do X, then I can find an A which is not a B

    So, if 1 and 2 are known to be true, it cannot be possible for me to do X; that is, X is impossible.


Problem3

Problem

  • All As are B

  • If I can do X, then I can find an A which is not a B

    So, if 1 and 2 are known to be true, it cannot be possible for me to do X; that is, X is impossible.


Problem4

Problem

  • All elliptic curves are modular

  • If I can find a solution to FLT, then I can find an elliptic curve which is not modular.

    So, if 1 (Taniyama-Shimura conjecture) and 2 (Fry’s e-conjecture) are true, then


Problem5

Problem

  • All elliptic curves are modular

  • If I can find a solution to FLT, then I can find an elliptic curve which is not modular.

    So, if 1 (Taniyama-Shimura conjecture) and 2 (Fry’s e-conjecture) are true, then it must be impossible to find a solution to FLT


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