B. Tech 2025 — Question Paper

Q1

Can a simple rule about even numbers create a perfect mathematical grouping? Let's look at this relation on integers, where x relates to y if their sum is even.

First, we check if it's reflexive. This means every number must relate to itself. If we plug in x for both spots, we get x plus x, which is two x. Since two times any integer is always even, the relation is definitely reflexive.

Next, is it symmetric? If x relates to y, does y relate to x? Well, if x plus y is even, then swapping them to y plus x gives the exact same sum. So yes, it's perfectly symmetric.