GATE 2025 CSE & IT Q49

Question

A = {0, 1, 2, 3, ...} is the set of non-negative integers. Let F be the set of functions from A to itself. For any two functions, f1, f2 ∈ F, we define
(f1⨀f2)(n) = f1(n) + f2(n)
for every number n in A. Which of the following is/are CORRECT about the mathematical structure (F,⨀)?

Accepted Answer

(F,⨀) is an Abelian monoid.

Answer

(F,⨀) is an Abelian group.

Answer

(F,⨀) is a non-Abelian group.

Answer

(F,⨀) is a non-Abelian monoid.