B. Tech 2025 — Question Paper

Q1

Ever wonder how we can neatly sort all integers into distinct families? Let's look at a relation where two integers, x and y, are connected if their sum is an even number.

Let's decode this rule before doing any heavy lifting. For the sum of two integers to be even, they must share the same 'parity'. That means they are either both even, or both odd.

To classify this relation, we test three properties. First: is it reflexive? Meaning, does every integer relate to itself?