If $R$ is an equivalence relation on a set $A$, then ${R^{ - 1}}$ is

Let $A =\{1,2,3,4,5,6,7\}$. Then the relation $R =$ $\{( x , y ) \in A \times A : x + y =7\}$ is

Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation in $A$ given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is

The minimum number of elements that must be added to the relation $R =\{( a , b ),( b , c )\}$ on the set $\{a, b, c\}$ so that it becomes symmetric and transitive is:

Let $A = \{1, 2, 3\}, B = \{1, 3, 5\}$. $A$ relation $R:A \to B$ is defined by $R = \{(1, 3), (1, 5), (2, 1)\}$. Then ${R^{ - 1}}$ is defined by

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