Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is

Let $R$ be the relation in the set $N$ given by $R =\{(a,\, b)\,:\, a=b-2,\, b>6\} .$ Choose the correct answer.

Let $H$ be the set of all houses in a village where each house is faced in one of the directions, East, West, North, South. Let $R = \{ (x,y)|(x,y) \in H \times H$ and $x, y$ are faced in same direction $\}$ . Then the relation $' R '$ is

Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $A$ such that $\mathrm{R} \subset \mathrm{S}$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is...............

Let $A =\{1,2,3,4,5,6,7\}$. Then the relation $R =$ $\{( x , y ) \in A \times A : x + y =7\}$ is

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

Relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3,4,5,6\}$ as $\mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{y}$ is divisible by $\mathrm{x}\}$