Let \( A=\{0,1,2,3\} \) and R be a relation on set A defined as \( R=\{(0,0),(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)\} \), then the relation R is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → reflexive and symmetric but not transitive.
Reflexive: (0, 0), (1, 1), (2, 2) and (3, 3) are all in R, so R is reflexive.
Symmetric: the pairs with different entries are (0, 1), (1, 0), (0, 3), (3, 0). Each comes with its reverse, so R is symmetric.
Transitive: (1, 0) and (0, 3) are in R, so transitivity would need (1, 3) in R.
\( \displaystyle (1,0)\in R,\ (0,3)\in R\ \text{but}\ (1,3)\notin R \)
So R is reflexive and symmetric but not transitive.
NCERT Exemplar:
Relations and Functions
