Let $R = \{ (3,\,3),\;(6,\;6),\;(9,\,9),\;(12,\,12),\;(6,\,12),\;(3,\,9),(3,\,12),\,(3,\,6)\} $ be a relation on the set $A = \{ 3,\,6,\,9,\,12\} $. The relation is

Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as $"ARB$ iff there exists a non-singular matrix $P$ such that $PAP ^{-1}= B "$ Then which of the following is true?

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $R$ in the set $A$ of human beings in a town at a particular time given by

$R =\{(x, y): x$ and $y$ live in the same locality $\}$

Show that the relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R =\{(a, b):|a-b|$ is even $\},$ is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to  each other and all the elements of $ \{2,4\}$ are

Give an example of a relation. Which is Transitive but neither reflexive nor symmetric.