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NEST2019MathematicsPermutation and Combination

Let n 2 be an integer and X= 1, , n . Define = : is a bijection of X and | (k)-k| 1 for all k X and for any , Y_ = m X: (m)=m . Then

Options

  1. Anumber of elements of is 1 if Y_ is empty for some
  2. Bfor every , ( (k))=k for all k X
  3. Cn is odd implies Y_ is non-empty for every
  4. Dn is even implies number of elements of Y_ is even for every

Correct answer

D. n is even implies number of elements of Y_ is even for every

Step-by-step solution

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