કોઈ ચોક્કસ સમયે કોઈ એક નગરમાં વસતા મનુષ્યોના ગણ $A$ પર વ્યાખ્યાયિત સંબંધ $R =\{(x, y): x$ એ $y$ ની પત્ની છે. $\} $ સ્વવાચક, સંમિત અથવા પરંપરિત સંબંધ છે કે નહિ તે નક્કી કરો ?

$R =\{( x , y ): x$ is the wife of $y \}$

Now,

$(x, x) \notin R$

since $x$ cannot be the wife of herself.

$\therefore R$ is not reflexive.

Now, let $(x, y) \in R$

$\Rightarrow x$ is the wife of $y$ Clearly y is not the wife of $x$. $\therefore $ $( y , x ) \notin R$

Indeed, if $x$ is the wife of $y$, then $y$ is the husband of $x$.

$\therefore $ $R$ is not transitive.

Let $( x , \,y ),\,( y , \,z ) \in R$

$\Rightarrow $ $x$ is the wife of $y$ and $y$ is the wife of $z$.

This case is not possible. Also, this does not imply that $x$ is the wife of $z$.

$\therefore $ $( x ,\, z ) \notin R$

$\therefore $ $R$ is not transitive.

Hence, $R$ is neither reflexive, nor symmetric, nor transitive.