Question

The relation "less than” in the set of natural numbers is

[UPSEAT 1994, 98, 99; AMU 1999]

• A. Only symmetric
• B. Only transitive
• C. Only reflexive
• D. Equivalence relation

Answer 1

The correct option is B

Only transitive

Since x < y , y < z $\Rightarrow$ x < z - x , y ,z $\in$ N

$\therefore$ xRy, yRz $\Rightarrow$ x R z , $\therefore$ Relation is transitive

$\therefore$ x < y does not give y < x .

$\therefore$ Relation is not symmetric.

Since x < x does not hold , hence relation is not relfexive .