@Arjun Sir
π(S) permutation is defined on N ,say,1234 and A is subset.How when π(A) ,say π(1,2,3) ,now there can be chance that in π permutation 1 is matching to 4,but above you said that π(1,2,3) will have only permutaions from 1,2,3 but in set A ,there is no 4.
As per asu comment above:-
let A = {1,2,3} then after applying π(A) = {123, 132, 213, 231, 312, 321}
Now i dont think π(A) will always have permutations from 1,2,3. May be in the N we have a permutations which maps,1->4 and so on.
(1,2,3,4)=>(4,3,1,2)// one example of permutation on N which will be applied to A and B