First slide

Relations XII

Question

The relation $R$ defined by $' >'$ on the set $N$ is

Moderate

A

reflexive
B

symmetric
C

transitive
D

equivalence relation

Solution

$2 > 2$ so $>$ is not reflexive, $3 > 2$ but $2 ⪇ 3$
so $(3, 2)$ $\in$ $R$ but $(2, 3)$ $\notin$ $R .$ Thus $R$ is not symmetric. If
$(a, b) \in R$ and $(b, c) \in R$ then $a > b, b > c$ fi $a$ > c so $(a, c)$
$\in R . R$ is not an equivalence relation

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