H= 5) Let H-(oES |0(4) -4] That is, H is the set of permutation in S, that leave the element 4 in its place. (i) Prove that H is a subgroup of S. (ii) Prove that S, is isomorphic to H. Explicitly give an isomorphism f: S, H listing the 6 elements of S, and giving the permutation in H to which it is sent under f. (iii) Show that S(P₁ *P₂) = S(P₁) */(P₂).

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A: Here we check associativity property.

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A:

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A:

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A:

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A:

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A:

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