The permutations p = (3 5 4), q= (1 5 2 3) and r = (1 5 2) are elements of S5. pal, m. (a) Find each of the following as a permutation in cycle form: wold wode of poq, poqop-¹, q². (b) State the order and parity of each of po q and q². (c) Determine, in cycle form, two permutations in S5 that conjugate p to r.

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A: Solution

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A: conjugate is where we change the sign in the middle of two terms . So ,conjugate is 3+2√5

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Q: 1a.) 0x**3  + 9x**3  1b.) 4X**3  - 9x**5  1c.) (3x   + 1x**3) + 2(9x**3 +(-3x)) 1d.)…

A: 1a.) 0x**3  + 9x**3 1b.) 4X**3  - 9x**5 1c.) (3x   + 1x**3) + 2(9x**3 +(-3x))1d.)…