JEE Mains Model Paper 4

We have R = {(x,_y) : x ∊ N, y ∊ N, 2x + y = 41}.
Domain ={1,2,3,.......,20}{∵ y ∊ N}
∴ R = {(1,39) , (2,37) , (3,35) ,......, (19,3) , (20,1)}
∴ Range = {1,3,5,....,39}
R is not reflexive as (2,2) ∉ R as 2 × 2 + 2 ≠41
Also R is not symmetric
As (1,39) ∊ R but (39,1 ) ∉ R
Further R is not transitive .
As(11,19) ∊ R,(19,3) ∊ R;but( 11,3) ∉ R
Hence . R is neither reflexive, nor symmetric and nor transitive