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

`2x+y = 41`

`=>x = (41-y)/2`

`:. y in {1,3,5,7....39}`, which is range of `R`.

`:. x in {1,2,3,4...19,10}`, which is domain of `R`.


Now,
`R = {(x,y): x,y in N and 2x+y = 41}`

Now, for `(a,a)`,

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