Question

2 points
Q12. If Rbe a relation defined
on natural number Nas R = {(x,
y):x+2y = 10, x, y both are
natural numbers} then the
domain and range of R
respectively is
O {2,4,6,8} and {4,3,2,1}
O {2,4,6,8} and {2,3,5,7}
O {2,4,7,9} and {4,3,2,1}
O {2,4,8} and {4,3,1}​

Answer 1

Step-by-step explanation:

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 .