Question

In the set $A=\{1,2,3,4,5\}$ a relation $R$ is defined by $R=\{(x, y) \mid x, y \in A$ and $x<y\}$. Then $R$ is

(A) Reflexive

(B) Symmetric

(C) Transitive 

(D) None of these

Answer 1

SOLUTION : Since $x \nless x$, therefore $R$ is not reflexive. Also $x<y$ does not imply that $y<x$, So $R$ is not symmetric.

Let $x R y$ and $y R z$. Then $x<y$ and $y<z \quad \Rightarrow \quad x<z$ i.e., $x R z$. Hence $R$ is transitive.