Question

Let $x,y\in I$ and suppose that a relation $R$ on I is defined by $x$ $R$ $y$ 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

Answer: (A)

$R$ is partial order relation

Since $x\le x$ for all $x\in I$
So $R$ is reflexive but is not symmetric as $(1,2)$ and $(2,1)$ $\notin R$
Also $R$ is transitive as $x\le y,y\le z\Rightarrow x\le z$