Question

Let $R=\left\{\right(x,y):x,y\in A,x+y=5\}$ where $A=\{1,2,3,4,5\}$, then

• A. $R$ is symmetric but not reflexive and transitive
• B. $R$ is an equivalence relation
• C. $R$ is reflexive, symmetric but not transitive
• D. $R$ is not reflexive, not symmetric but transitive

Answer 1

Answer: (A)

$R$ is symmetric but not reflexive and transitive

$R=\{(1,4),(4,1),(2,3)(3,2)\}$
so $R$ is not reflexive as $(1,1)\notin R$
$R$ is symmetric by defination and $R$ is not transitive
as $(1,4)\in R$, $(4,1)\in R$ but $(1,1)\notin R$