Let R be the relation on the set {1, 2, 3, 4} defined by R = {(1, 2), (2, 1), (2, 2), (3, 3), (4, 4), (1, 4), (4, 1)}. Then R is:
Answer & explanation
Correct answer: option 2
Given set $A=\{1,2,3,4\}$
$R=\{(1,2),(2,1),(2,2),(3,3),(4,4),(1,4),(4,1)\}$
Reflexive:
For reflexive relation, $(1,1),(2,2),(3,3),(4,4)$ must be present.
$(1,1)$ is missing.
Hence, $R$ is not reflexive.
Symmetric:
If $(a,b)\in R$ then $(b,a)\in R$.
$(1,2)$ and $(2,1)$ ✓
$(1,4)$ and $(4,1)$ ✓
Thus $R$ is symmetric.
Transitive:
$(1,2)$ and $(2,1)$ imply $(1,1)$ which is not in $R$.
Hence $R$ is not transitive.
final answer: The relation is symmetric but neither reflexive nor transitive.