# Q.1 Determine whether each of the following relations are reflexive, symmetric and transitive:(v). Relation R in the set A of human beings in a town at a particular time given by(d) $R = \{(x, y) : x\;is\;wife\;of\;y\}$

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

$\left ( x,y \right ) \in R$ means $x\;is\;wife\;of\;y$ but  $x\;is\;not\, wife\;of\;x$ i.e.$\left ( x,x \right ) \notin R$.

So, it is not reflexive.

$\left ( x,y \right ) \in R$ means $x\;is\;wife\;of\;y$ but  $y\;is\;not\, wife\;of\;x$ i.e.$\left ( y,x \right ) \notin R$.

So, it is not symmetric.

Let, $\left ( x,y \right ),\left ( y,z \right ) \in R$ means $x\;is\;wife\;of\;y$ and $y\;is\;wife\;of\;z$.

This case is not possible so it is not transitive.

Hence, it is not  reflexive, symmetric and
transitive.

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