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 $S$ be the set of all real numbers. $A$ relation $R$ has been defined on $S$ by $a R b \Leftrightarrow |a-b| \leq 1$. Then $R$ is:

Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R\beta \Leftrightarrow \alpha \perp \beta$,where $\alpha, \beta \in L$. Then $R$ is

Let $P(S)$ denote the power set of $S = \{1, 2, 3, \ldots, 10\}$. Define the relations $R_1$ and $R_2$ on $P(S)$ as $A R_1 B$ if $(A \cap B^c) \cup (B \cap A^c) = \varnothing$ and $A R_2 B$ if $A \cup B^c = B \cup A^c, \forall A, B \in P(S)$. Then:

If $R = \{(6, 6), (9, 9), (6, 12), (12, 12), (12, 6)\}$ is a relation on set $A = \{3, 6, 9, 12\}$,then relation $R$ is

Let $A$ be the set of all students of a boys' school. Show that the relation $R$ in $A$ given by $R = \{(a, b) : a \text{ is sister of } b\}$ is the empty relation and $R^{\prime} = \{(a, b) : \text{the difference between heights of } a \text{ and } b \text{ is less than } 3 \text{ meters}\}$ is the universal relation.