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Which one of the following statements is true?
  • a)
    Every permutation is a cycle
  • b)
    Every cycle is a permutation
  • c)
    Sn is not cyclic for all n
  • d)
    Every permutations s ∈ Sn can be written as product of (n - 1) transposition
Correct answer is option 'B,C,D'. Can you explain this answer?
Verified Answer
Which one of the following statements is true?a)Every permutation is a...
We know that every cycle is permutation but every permutation is not a cycle and it is also true that Sn is not cyclic for all n and every permutation s ∈ Sn can be written as product of (n -1) transposition.
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Which one of the following statements is true?a)Every permutation is a...
Sn is cyclic for n=2, so option c is wrong. In S3, you cannot write (12) as a product of 2 transpositions, so option d is wrong. Answer should be only B.
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Community Answer
Which one of the following statements is true?a)Every permutation is a...
B) Every cycle is a permutation.
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Which one of the following statements is true?a)Every permutation is a cycleb)Every cycle is a permutationc)Sn is not cyclic for all nd)Every permutations s ∈Sn can be written as product of (n - 1) transpositionCorrect answer is option 'B,C,D'. Can you explain this answer?
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