Vinod Singh and Shweta Pawar Solutions for Chapter: Sets, Relations and Functions, Exercise 3: Competitive Thinking

If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7,$ then the number of relations from $A$ to $B$ is 

If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A\times B$ and $B\times A$ are

Let $A=\{x, y, z\}$ and $B=\{a, b, c, d\}$ Which one of the following is not a relation from $A$ to $B?$

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation, it is sufficient, if $R$

Let a relation $R$ in the set $N$ of natural numbers be defined as $\left(x,y\right)\iff x^2-4xy+3y^2=0 \forall x, y\in N$. The relation $R$ is

Let $A=\{2,4,6,8\}.$ A relation $R$ on $A$ is  $R=\left\{\right(2,4),(4,2),(4,6),(6,4\left)\right\}.$ Then $R$ is 

The relation $R$ defined in $N$ as $aRb\iff b$ is divisible by $a$ is

Let $R=\left\{\right(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6\left)\right\}$ for  $A=\{3,6,9,12\}$. Then the relation is