GUJCET 2024 Math Paper (04)

Concept:Check the properties of reflexivity, symmetry, and transitivity for the given relation.Explanation:The relation is $R = \{(a,a),(b,b),(c,c),(a,c)\}$ on $A = \{a,b,c\}$.Reflexive: Every element is related to itself, since $(a,a),(b,b),(c,c) \in R$. So $R$ is reflexive.Symmetric: $(a,c) \in R$, but $(c,a) \notin R$. So $R$ is not symmetric.Transitive: The only non-diagonal pair is $(a,c)$, and combining it with existing pairs gives no missing required pair. So $R$ is transitive.Thus, $R$ is reflexive and transitive but not symmetric.Answer:Reflexive and transitive but not symmetric