Question

Given $A=\{2,3,5\}$ and $B=\{6,10,14,18\}$ ; find the number of elements in relation $R$ such that $R=\left\{\right(x,y)ϵA\times B,x<y\text{and}\frac{y}{x}ϵN\}$

Answer 1

Given, $A=\{2,3,5\}$ and $B=\{6,10,14,18\}$

Product of two sets is the set of ordered pairs formed by mapping every element from the first set to every element of the second set.
So, $A\times B=\left\{\right(2,6),(2,10),(2,14),(2,18),(3,6),(3,10),(3,14),(3,18),(5,6),(5,10),(5,14),(5,18\left)\right\}$.
Now, a Relation on this set of ordered pairs of $A\times B$, where $x<y$ and $\frac{y}{x}$ is a natural number will be
$R=\left\{\right(2,6),(2,10),(2,14),(2,18),(3,6),(3,18),(5,10\left)\right\}$

Thus, the number of elements in $R$ is $7$.