First slide

Relations XII

Question

The relation 'less than' on the set of natural numbers is

Moderate

A

Only symmetric
B

Only transitive
C

Only reflexive
D

Equivalence relation

Solution

$\begin{array}{l} As x < y, y < z \Rightarrow x < z \forall x, y, z \in N \\ ∴ x R y, y R z \Rightarrow x R z, ∴ Relation is transitive \\ ∴ x < y does not give y < x, \end{array}$
$∴ Relation is not symmetric$
$As x < x does not hold, hence relation is not reflective$

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