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Let $X$ be the set of all persons living in a city. Persons $x$, in $X$ are said to be related as $x < y$ if $y$ is at least 5 years older than $x$. Which one of the following is correct?
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Verified Answer
The correct answer is:
The relation is transitive but neither reflexive nor symmetric
Given that $x < y$ if $y \geq x+5$ For Reflexive:
$x < x$
Hence, relation is not reflexive For Symmetry:
if $x < y$
then $y < x$
Hence, relation is not symmetry.
ForTransitive:
if $x < y$ and $y < z$
then $\mathrm{x} < 2$
Hence, relation is transitive
$x < x$
Hence, relation is not reflexive For Symmetry:
if $x < y$
then $y < x$
Hence, relation is not symmetry.
ForTransitive:
if $x < y$ and $y < z$
then $\mathrm{x} < 2$
Hence, relation is transitive
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