Let $R$ be a reflexive relation on a set $A$ and $I$ be the identity relation on $A$. Then

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:

Let $R$ and $S$ be two equivalence relations on a set $A$. Then

Let $n$ be a fixed positive integer. The relation $R$ on the set of integers $Z$ is defined by $aRb \Leftrightarrow n | (a - b)$. Then $R$ is:

The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is

Let $T$ be the set of all triangles in a Euclidean plane and a relation $R$ on $T$ is defined as $aRb$ if and only if $a \sim b$ (where $a \sim b$ denotes that triangle $a$ is similar to triangle $b$) for all $a, b \in T$. Then $R$ is: