Question

Let R be a relation on the set N be defined by $\left\{\right(x,y)|x,y|N,2x+y=41\}$. Then R is

• A. Reflexive
• B. Symmetric
• C. Transitive
• D. None of these

Answer 1

The correct option is D

None of these

On the set N of natural numbers,

R = {(x,y): x,y $\in$ N , 2x + y = 41}.

Since (1,1) $\notin$ R as 2.1+1 = 3 $\ne$ 41. So R is not reflexive.

(1,39) $\in$ R But (39,1) $\notin$ R . So R is not symmetric, (20,1)

(1,39) $\in$ R . But (20,39) $\notin$ R. So R is not transitive .