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

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

Give an example of a relation which is transitive but neither reflexive nor symmetric.

Let $R$ be a relation on a set $A$ such that $R = R^{-1}$. Then $R$ is:

For any two real numbers $a$ and $b$,we define $a R b$ if and only if $\sin ^{2} a+\cos ^{2} b=1$. The relation $R$ is

Let $A = \{0, 1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\max\{x, y\} \in \{3, 4\}$. Then among the statements $(S_1)$: The number of elements in $R$ is $18$,and $(S_2)$: The relation $R$ is symmetric but neither reflexive nor transitive: