Let `R` be a relation defined on the set of natural numbers N as `R={(x , y): x , y in N ,2x+y=41}` Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) transitive.

Explanation

To solve the problem step by step, we will analyze the relation \( R \) defined on the set of natural numbers \( \mathbb{N} \) by the equation \( 2x + y = 41 \).

### Step 1: Find the Domain of \( R \)

The relation \( R \) consists of ordered pairs \( (x, y) \) such that \( 2x + y = 41 \). We need to find the values of \( x \) (the first element of the ordered pair) that yield a corresponding natural number \( y \).

1. Rearranging the equation gives us:
\[
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