Question

Let a set $A = A _{1} \cup A _{2} \cup \ldots \cup A _{k^{\prime}}$ where $A_{i} \cap A_{j}=\phi$ for $i \neq j 1 \leq i, j \leq k$. Define the relation $R$ from $A$ to $A$ by $R=\left\{(x, y): y \in A_{i}\right.$ if and only if $\left.x \in A_{i}, 1 \leq i \leq k\right\}$. Then, $R$ is :

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

Answer 1

Answer: (D)

$A=\{1,2,3\}$
$R=\{(1,1),(1,2),(1,3)(2,1),(2,2),(2,3)(3,1)(3,2)(3,3)\}$