12 As in Example 75 let X be the set of permutations of n an

12. As in Example 7.5, let X be the set of permutations of n and say that o EX satisfies property if o(i) Example 7.5. Let m be a fixed positive integer and let X consist of all bijections from m] to [m]. Elements of X are called permutations. Then for each i 1,2 and each permutation o EX, we say that or satisfies P if o(i i. For example, the permutation or of 5 given in by the table below satisfies Ps and and no other P 1 2 3 4 5 o(i) 2 4 3 1 5 in-context ./knowl/exa inclusion-exclusion prop-derange.html

Solution

consider Permutaion T:[8]--->[8]

define by disjoint cycles (2 5 3 6 7 )

that is i------> 1 2 3 4 5 6 7 8

maps T(i)--->1 5 6 4 3 7 2 8

this example P₁ that is T(1)=1

P₄  that is T(4)=4

and P₈ that is T(8)=8