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  3. 4. (a) suppose that ??=(1 5 2 3)(4) and ??=(1 2 4

4. (a) Suppose that ??=(1 5 2 3)(4) and ??=(1 2 4 5)(3) in S5. If ?1...

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Advance Math

4.
(a) Suppose that ??=(1 5 2 3)(4) and ??=(1 2 4 5)(3) in S5. If?1 = 2, find ? and ?.
(b) In Sn, show that ? = ? if and only if ?(?)^(?1) = ?. ? isthe identity permutation. Must be written as a proof.
(c) Let ?=(1 2 3) and ?=(1 2) in S3. Show thatS3={?,?,?^2,?,??,?(?)^2} and that ?^3=?=?^2 and ??=?(?)^2, thenfill out the multiplication table for S3.

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