Consider a non-empty set A. Prove that S(A) is closed in (M(A),o).
Meaning: "o" is the composition of functions which defines a binary operation on M(A), the set of all maps from A to A. You need to prove that the set of all permutations on A is closed under the composition.
Inverses exist in S(A) because each f : A --> A in S(A) is bijective, hence has an ...
Permutations, Binary Operations and Mappings are investigated. The solution is detailed and well presented.