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\}

Answers (1)

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.

 

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