The relation $R$ defined on the set $A = \{1, 2, 3, 4, 5\}$ by $R = \{(x, y)$ : $|{x^2} - {y^2}| < 16\} $ is given by

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $R$ in the set $A$ of human beings in a town at a particular time given by

$R =\{(x, y): x$ and $y$ live in the same locality $\}$

Let $R _{1}=\{( a , b ) \in N \times N :| a - b | \leq 13\}$ and $R _{2}=\{( a , b ) \in N \times N :| a - b | \neq 13\} .$ Thenon $N$

The relation "congruence modulo $m$" is

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 $R$ iff ${l_1}$ is parallel to ${l_2}$. Then the relation $R$ is

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