Discrete Mathematics questions – GATE 2025 Let R be the relation on the set of positive integer.

Discrete Mathematics questions – GATE 2015 Let R be the relation on the set of positive integer.

Great! You’re referring to a Discrete Mathematics question likely from the GATE 2025 syllabus. You mentioned:

“Let $R$ be the relation on the set of positive integers…”

Please provide the full question, including the definition of the relation $R$, and what the question is asking (e.g., Is $R$ reflexive, symmetric, transitive? Find the number of equivalence classes? etc.)

In the meantime, here’s a general template for such problems:

Example Problem Format

Let $R$ be a relation on the set of positive integers Z+\mathbb{Z}^+Z+, defined by:

$(a,b)\in R⟺a\mathrm{mod}n=b\mathrm{mod}n$

Then $R$ is:

Solution:
This is the standard congruence modulo n relation.

• Reflexive: Yes, because $a\mathrm{mod}n=a\mathrm{mod}n$

• Symmetric: Yes, if $a\equiv b(\mathrm{mod}n)$, then $b\equiv a(\mathrm{mod}n)$

• Transitive: Yes, if $a\equiv b(\mathrm{mod}n)$ and $b\equiv c(\mathrm{mod}n)$, then $a\equiv c(\mathrm{mod}n)$

Hence, it is an equivalence relation

Please share the full question so I can give you a specific solution!

Discrete Mathematics questions – GATE 2025 Let R be the relation on the set of positive integer.

Problems on Discrete Mathematics1 (Part I)