Question

The relation $R$ is defined in the set $\{1,2,3,4,5,6\}$ as $R=\{(a,b):b=a+1\}$, then

• A. $R$ is neither reflexive nor symmetric nor transitive
• B. $R$ is neither reflexive nor symmetric but transitive
• C. $R$ is not reflexive but symmetric and transitive
• D. $R$ is reflexive, symmetric and transitive

Answer 1

Answer: (A)

Let, $A=\{1,2,3,4,5,6\}$
The relation $R$ is defined on set $A$ is $R=\{(a,b):b=a+1\}$.
Therefore, $R=\{(1,2),(2,3),(3,4),(4,5),(5,6)\}$
Now, $6\in A$ but $(6,6)\notin R$.
Therefore, $R$ is not reflexive.
It can be observed that $(1,2)\in R$ but $(2,1)\notin R$.
Therefore, $R$ is not symmetric.
Now, $(1,2),(2,3)\in R$ but $(1,3)\notin R$.
Therefore, $R$ is not transitive.
Hence, $R$ is neither reflexive nor symmetric nor transitive.