First slide

Relations XII

Question

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

Moderate

A

$R$ is reflexive but not symmetric
B

$R$ is an equivalence relation
C

$R$ is neither reflexive nor symmetric
D

$R$ is symmetric but not transitive

Solution

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

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