First slide

Relations XII

Question

Let $R$ be a relation on $R$ defined as $a R b$ if $|a| \leq b .$ Then, relation $R$ is

Moderate

A

reflexive
B

symmetric
C

transitive
D

not antisymetric

Solution

If $a = - 1$ than a is not related to a. So $R$ is not reflexive. If $a = - 1, b = 2$ then $|a| \leq b$ but $|b| > a,$ so $R$ is not symmetric. If $|a| \leq b$ and $|b| \leq c$ then $|a| \leq b$ $|b| \leq c$ so $|a| \leq c,$ hence a is related to $c$ . Thus $R$ is transitive. If $|a| \leq b$ , and $|b| \leq c$ then $a \leq |a| \leq b \leq |b| \leq a .$ So $a = b$ , $R$ is anti symmetric.

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