Question

Let S denote set of all integers. Define a relation R on S as 'aRb if $a{b}^2\ge 0$ where $a,b\in S$'.
Then R is :

• A. Reflective but neither symmetric nor transitive relation
• B. Reflective, symmetric but nor transitive relation
• C. An equivalence relation
• D. None of these

Answer 1

The correct option is D None of these

The relation is not reflective as every element is $aRb$ not $aRa$.

The relation is not symmetric as every element is $aRb\ne bRa$ i.e. solutions are non-unique.

The relation is transitive as every relation $aRb$ and $bRc⟹aRc$.