Question

The relation $R = \{(1$, $1)$, $(2$, $2) (3$, $3)$, $(1$, $2)$, $(2$, $3)$, $(1$, $3)\}$ on set $A = \{1$, $2$, $3\}$ is

• A. Reflexive but not symmetric
• B. Reflexive but not transitive
• C. Symmetric and transitive
• D. Neither symmetric nor transitive

Answer 1

Answer: (A)

Reflexive : $(1$, $1)$, $(2$, $2)$, $(3$, $3) \in R$, $R$ is reflexive
Symmetric : $(1$, $2) \in R$ but $(2$, $1) \notin R$, $R$ is not symmetric.
Transitive : $(1$, $2) \in R$ and $(2$, $3) \in R$
$ \Rightarrow (1$, $3) \in R$, $R$ is transitive.