Let $R$ be a transitive relation on a set $A$ and $I$ be the identity relation on $A$. Then:

Let $A$ be a non-empty set of children in a family. The relation $R$ is defined on $A$ as '$x$ is a brother of $y$'. This relation is:

Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $R = \{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}$. Find the domain of $R$.

Let $R$ be a relation from $Q$ to $Q$ defined by $R = \{(a, b) : a, b \in Q \text{ and } a - b \in Z\}$. Show that $(a, b) \in R$ implies that $(b, a) \in R$.

Let ${R_1}$ be a relation defined by ${R_1} = \{ (a, b) | a \ge b, a, b \in R \}$. Then ${R_1}$ is

Let $A = \{1, 2, 3, \ldots, 100\}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $2x = 3y$. Let $R_1$ be a symmetric relation on $A$ such that $R \subset R_1$ and the number of elements in $R_1$ is $n$. Then,the minimum value of $n$ is: