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Vijay posted an Question
December 15, 2021 • 11:45 am 30 points
  • IIT JAM
  • Mathematics (MA)

Sp2019;55. please send the solution to the problem given in the attachment.

SP2019;55. please send the solution to the problem given in the attachment.

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  • Anonymous User Best Answer

    check attachment

    cropped5895079594543419416.jpg
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    no. of elements in the set pata karna hai where x^4=e kaise pata karenge sir?

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    given x⁴=e means order of X is 4 we find 4 order elements of S3 in set

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    {e, (12) ,(23),(13)} sir i think these 4 elements in S3 gives identity in there 4th power .. question is not asking about order 4 element ... it says how many elements give identity in there 4 power... i am just thinking (kya yese v ho sakta hai)

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    {e, (12) ,(23),(13)} 4 power of thses elements is e

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    4th power tak check karne me bahut time nahi chalajaega is there a short trick ?

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    short trick order hai (1,2) ka order 2 hai so x²=e ab iski power kuch bhi lo e hi aayga

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    each element ka order calculate karo

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    exactly there are 4 elements is S3 whose 4th power is Identity... so i think ans is 4

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    Navdeep sir isme short trick kaha hai?

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    (1,2) 2 length ka permutations hai so iska order 2 hai I.e (1,2)²=e (1,2)⁴=e

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    order 3 wala element identity qu nahi hoga sir?

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    3 order ke liye x³=e hoga

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    haan par hamare set me toh 4 order wala element hai he nahi na toh x^4 =e kaise milega?

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    2 order ke elements hai so x²=e => x⁴=e

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