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:

Let $R$ be a relation over the set $N \times N$ and it is defined by $(a, b)R(c, d) \iff a + d = b + c$. Then $R$ is

The relation $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ 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:

Let ${R_1}$ be a relation defined by ${R_1} = \{ (a, b) | a \ge b, a, b \in R \}$. Then ${R_1}$ is

Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is