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  4. The relation ‘less than’ in the set of natural numbers is

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Q. The relation ‘less than’ in the set of natural numbers is

Relations and Functions - Part 2

Solution:

The relation ‘less than’ is only transitive because
$x< y, y< z $
$\Rightarrow x < z , x, y, z \in N$
$ \therefore x\, R\, y, y\, R\, z $
$\Rightarrow x \,R\, z$