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.

Answer

N/a

Explanation

Given that, ` R={(x,y):x in N, y in N, 2x +y=41}.`
Domain ` ={1,2,3, …, 20}`
Range `={1,3,5,7,…,39}`
`R={(1,39),(2,37),(2,35),…,(19,3),(20,1)}`
R is not reflexive as `(2,2) notin R`
`2xx2+2 ne 41`
So, R is not synmmetric.
As `(1,39) in R ` but `(39,1) notin R`
So, R is not transitive.
As `(11,19) in R, (19,3) in R`
But `(11,3) notin R`
Hence, R is neither reflexive nor symmetric and nor transitive.