In the set $A = \{1, 2, 3, 4, 5\}$,a relation $R$ is defined by $R = \{(x, y) | x, y \in A \text{ and } x < y\}$. Then $R$ is

Let $A = \{1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $x R y$ if and only if $4x \leq 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m+n$ is equal to:

Let $R$ and $S$ be two equivalence relations on a non-void set $A$. Then

$A$ relation $R$ on the set of natural numbers is defined as $\{(a, b) : |a - b| = 3\}$. Then $R$ is:

Check whether the relation $R$ in $\mathbb{R}$ defined by $R = \{(a, b) : a \leq b^3\}$ is reflexive,symmetric,or transitive.

Let $n$ be a fixed positive integer. Define a relation $R$ on the set $Z$ of integers by $aRb \Leftrightarrow n | (a - b)$. Then $R$ is