The relation $R$ defined on the set of natural numbers as $\{(a, b) : a\}$ differs from $b$ by $3\}$ is given by

Let $L$ be the set of all straight lines in the Euclidean plane. Two lines $l_1$ and $l_2$ are said to be related by the relation $R$ if and only if $l_1$ is parallel to $l_2$. Then the relation $R$ is

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $N$ of natural numbers defined as
$R = \{(x, y) : y = x + 5 \text{ and } x < 4\}$

Let $\rho_{1}$ and $\rho_{2}$ be two equivalence relations defined on a non-void set $S$. Then

Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$. Let $R$ be a relation on $A$ defined by $x R y$ if and only if $0 \leq x^2 + 2y \leq 4$. Let $l$ be the number of elements in $R$ and $m$ be the minimum number of elements required to be added to $R$ to make it a reflexive relation. Then $l+m$ is equal to

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