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, f_1, f_2 ∈ F, we define (f_1 f_2)(n) = f_1(n) + f_2(n) for every number n in A. Which of the following is/are CORRECT about the mathematical structure (F, )?

GATE CSE 2025 Session 1 Q49: Algebraic structure of functions under pointwise addition

Engineering Mathematics
2 marks
MSQ
No negative marking

$A = \{0, 1, 2, 3, \ldots\}$ is the set of non-negative integers. Let $\mathcal{F}$ be the set of functions from $A$ to itself. For any two functions, $f_1, f_2 \in \mathcal{F}$ , we define

$(f_1 \odot f_2)(n) = f_1(n) + f_2(n)$

for every number $n$ in $A$ . Which of the following is/are CORRECT about the mathematical structure $(\mathcal{F}, \odot)$ ?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

Show answer and explanation

Answer: B (official GATE 2025 final answer key)

Concept used: Pointwise addition inherits closure, associativity, commutativity and identity from $(A, +)$ , but not inverses.

First step: The zero function is the identity; check whether a function like $f(n) = 1$ has an inverse whose values stay non-negative.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

PracticePractise Engineering Mathematics questions →Full paperAll GATE CSE 2025 Session 1 questions →

GATE CSE 2025 Session 1 Q49: Algebraic structure of functions under pointwise addition

Question

Full step-by-step solution

More Engineering Mathematics PYQs