R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)} on A={1,2,3,4}

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Let R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)} be a relation on set A={1,2,3,4}. Then relation R is?

Answer:

R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)}

It is seen that $(a,a)\notin R$ , for every $a∈\{1,2,3,4\}.$

∴ R is not reflexive.

It is seen that $(1,3)∈R$ , but $(3,1)$ $\notin$ R.

∴ R is not symmetric.

Also, it is observed that $(a,b),(b,c)\in R⇒(a,c)\notin R\text{ for all }a,b,c∈\{1,2,3,4\}$

∴ R is not transitive.

Hence,R neither is reflexive nor transitive nor symmetric.