1. Determine whether each of the following relations are reflexive, symmetric and
transitive:

(iii) Relation R in the set A = \{1,2,3,4,5,6\} as R = \{(x,y) : y \; \textup{is} \; divisible \; by\; x\}

Answers (1)

A = \{1,2,3,4,5,6\}

R = \left \{ \left ( 2,4 \right ),\left ( 3,6 \right ),\left ( 2,6 \right ),\left ( 1,1 \right ),\left ( 2,2 \right ),\left ( 3,3 \right ),\left ( 4,4 \right ),\left ( 5,5 \right ),\left ( 6,6 \right )\right \}

Any number is divisible by itself  and  \left ( x,x \right ) \in R.So it is  reflexive.

\left ( 2,4 \right ) \in R but \left ( 4,2 \right ) \notin R .Hence,it is not symmetric.

\left ( 2,4 \right ),\left ( 4,4 \right ) \in R and  4 is divisible by 2 and 4 is divisible by 4.

Hence,it is transitive.

Hence,it is reflexive and  transitive but not symmetric.

 

 

 

 

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