$A$ relation $R$ on a non-empty set $A$ is an equivalence relation if $R$ is:

Let $R$ be the relation in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3)\}$. Choose the correct answer.

Let $R$ be a relation defined on $N \times N$ by $(a, b) R(c, d) \Leftrightarrow a(b + d) = c(b + d)$ is incorrect,the correct relation is $(a, b) R(c, d) \Leftrightarrow ad = bc$. Given the relation $(a, b) R(c, d) \Leftrightarrow a(b + d) = c(a + d)$ is not standard,let us analyze the relation $(a, b) R(c, d) \Leftrightarrow ad = bc$. Then $R$ is:

Let $L$ be the set of all lines in a plane and $R$ be the relation in $L$ defined as $R = \{(L_{1}, L_{2}) : L_{1} \text{ is perpendicular to } L_{2}\}$. Show that $R$ is symmetric but neither reflexive nor transitive.

Let $R = \{(1,2), (2,3), (3,3)\}$ be a relation defined on the set $A = \{1, 2, 3, 4\}$. Then the minimum number of elements needed to be added to $R$ so that $R$ becomes an equivalence relation is:

$A$ relation $R$ on the set of natural numbers is defined as $\{(a, b) : |a - b| = 3\}$. Then $R$ is: