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###### Vijay posted an Question
December 15, 2021 • 06:15 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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• ##### Navdeep goyal 1 Best Answer

check attachment

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

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

{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)

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

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

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

each element ka order calculate karo

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

Navdeep sir isme short trick kaha hai?

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

order 3 wala element identity qu nahi hoga sir?

3 order ke liye x³=e hoga

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

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

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