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 

(c) R = \{(x, y) : x\;is\;exactly\;7\;cm\;taller\;than\;y\}

Answers (1)

R = \{(x, y) : x\;is\;exactly\;7\;cm\;taller\;than\;y\}

\left ( x,y\right )\in R means x\;is\;exactly\;7\;cm\;taller\;than\;y but x\;is\;not\;\;taller\;than\;x i.e. \left ( x,x \right )\notin R.So, it is not reflexive.

\left ( x,y\right )\in R means x\;is\;exactly\;7\;cm\;taller\;than\;y  but y\;is\;not\;\;taller\;than\;x i.e  \left ( y,x \right )\notin R.So, it is not symmetric.

\left ( x,y\right ),\left ( y,z \right )\in R means x\;is\;exactly\;7\;cm\;taller\;than\;y and y\;is\;exactly\;7\;cm\;taller\;than\;z.

x\;is\;exactly\;14\;cm\;taller\;than\;z  i.e.  \left ( x,z \right )\notin R.

Hence,it is not reflexive,not symmetric and
not transitive.

 

 

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