Let the relation $R$ on the set $M = \{1, 2, 3, \dots, 16\}$ be given by $R = \{(x, y) : 4y = 5x - 3, x, y \in M\}$. Then the minimum number of elements required to be added in $R$, in order to make the relation symmetric, is equal to

Which of the following is not correct for relation $R$ on the set of real numbers?

Consider the relation $R$ on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab > 0$. Then, among the statements:
$I$. The number of elements in $R$ is $17$
$II$. $R$ is an equivalence relation

Let $R = \{(3, 3), (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$ be a relation on the set $A = \{3, 5, 9, 12\}.$ Then,$R$ is

Let $A = \{1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $x R y$ if and only if $4x \leq 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m+n$ is equal to:

Let $A = \{0, 3, 4, 6, 7, 8, 9, 10\}$ and $R$ be the relation defined on $A$ such that $R = \{(x, y) \in A \times A : x - y \text{ is an odd positive integer or } x - y = 2\}$. The minimum number of elements that must be added to the relation $R$ so that it becomes a symmetric relation is equal to $...........$.