Define a relation $R$ on $A=\{1, 2, 3, 4\}$ as $x R y$ if $x$ divides $y$. $R$ is

Let $R = \{( P , Q ) \mid P \text{ and } Q \text{ are at the same distance from the origin} \}$ be a relation. Then the equivalence class of $(1, -1)$ is the set:

Let $A = \{1, 2, 3, 4\}$ and $R = \{(2, 2), (3, 3), (4, 4), (1, 2)\}$ be a relation on $A$. Then $R$ is:

Let $A = \{p, q, r\}$. Which of the following is $NOT$ an equivalence relation on $A$?

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

Let $L$ be the set of all lines in a plane and $R$ be the relation in $L$ defined as $R = \{(L_{1}, L_{2}) : L_{1} \text{ is perpendicular to } L_{2}\}$. Show that $R$ is symmetric but neither reflexive nor transitive.