Question

Let $x,y\in I$ and suppose that a relation $R$ on $I$ is defined by $xRy$ if and only if $x\le y$ then

• A. $R$ is partial order relation
• B. $R$ is an equivalence relation
• C. $R$ is reflexive and symmetric
• D. $R$ is symmetric and transitive

Answer 1

The correct option is A $R$ is partial order relation

Since $x\le y$ for all $x\in R$, so $R$ is reflexive

but is not symmetric as $(1,2)\in R$ and $(2,1)\notin R$.

Also $R$ is transitive as $x\le y,y\le z\Rightarrow x\le z$