Question

Invariant permutations of two functions can form __________

(a) groups

(b) lattices

(c) graphs

(d) rings

This question was addressed to me during an interview.

I need to ask this question from Groups topic in section Groups of Discrete Mathematics

Answer 1

The correct option is (a) groups

Explanation: Suppose, there are two functions f1 and f2 which belong to the same equivalence class since there exists an invariant permutation say, π(a permutation that does not change the object itself, but only its representation), such that: f2*π≡f1. So, invariant permutations can form a group, as the product (composition) of invariant permutations is again an invariant permutation.