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

$A$ relation $R$ is defined on the set of natural numbers such that $m$ is related to $n$ if $m$ is a multiple of $n$. Then the relation is:

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, b) \in R, (b, c) \in R$ implies $(a, c) \in R$

Let $A = \{-2, -1, 0, 1, 2, 3\}$. Let $R$ be a relation on $A$ defined by $x R y$ if and only if $y = \max \{x, 1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added to $R$ to make it reflexive and symmetric,respectively. Then $l + m + n$ is equal to

The number of reflexive relations on a set with $4$ elements is equal to

Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm \iff n$ is a factor of $m$ (i.e.,$n|m$). Then $R$ is