A relation \( R \) on set of real numbers \( (\mathrm{R}) \) is defined as \( R=\{(a,b):a\le b,\ a,b\in\mathrm{R}\} \), The relation is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Reflexive and transitive but not symmetric
Reflexive: \( a\le a \) for every real a, so \( (a,a)\in R \). R is reflexive.
Symmetric: \( (1,2)\in R \) since \( 1\le 2 \), but \( (2,1)\notin R \) since \( 2\le 1 \) is false. R is not symmetric.
Transitive: if \( a\le b \) and \( b\le c \), then \( a\le c \). R is transitive.
So R is reflexive and transitive but not symmetric.