Let $A = \{ 2,\,4,\,6,\,8\} $. $A$ relation $R$ on $A$ is defined by $R = \{ (2,\,4),\,(4,\,2),\,(4,\,6),\,(6,\,4)\} $. Then $R$ 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

If $R$ is an equivalence relation on a set $A$, then ${R^{ - 1}}$ is

Give an example of a relation. Which is Symmetric and transitive but not reflexive.

Let $A =\{2,3,4,5, \ldots ., 30\}$ and $^{\prime} \simeq ^{\prime}$ be an equivalence relation on $A \times A ,$ defined by $(a, b) \simeq (c, d),$ if and only if $a d=b c .$ Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to :

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

$R =\{(x, y): x$ is wife of  $y\}$