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(a) $R = \{(x,y) : x \;and\; y\;work\;at\;the\;same\;place\}$

$R = \{(x,y) : x \;and\; y\;work\;at\;the\;same\;place\}$

$\left ( x,x \right )\in R$,so it is reflexive

$\left ( x,y \right )\in R$ means $x \;and\; y\;work\;at\;the\;same\;place$ .

$y \;and\; x\;work\;at\;the\;same\;place$ i.e. $\left ( y,x \right )\in R$ so it is symmetric.

$\left ( x,y \right ),\left ( y,z \right )\in R$ means $x \;and\; y\;work\;at\;the\;same\;place$ also $y \;and\; z\;work\;at\;the\;same\;place$.It states that $x \;and\; z\;work\;at\;the\;same\;place$ i.e. $\left ( x,z \right )\in R$.So, it is transitive.

Hence, it is  reflexive, symmetric and
transitive.

Exams
Articles
Questions