Sets Relations And Functions Question 61
Question: Let $R$ be a relation on the set $N$ be defined by $\{(x, y) \mid x, y \in N, 2 x+y=41\}$. Then prove that the $R$ is
Options:
A) Reflexive
B) Symmetric
C) Transitive
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
- 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.
BETA
