Let R_{1} and R_{2} be relations on the set { | vedclass

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Question

Here, $p , p ^{ n } \in\{1,2, \ldots 50\}$

Now p can take values

$2,3,5,7,11,13,17,23,29,31,37,41,43$ and $47 .$

we can calculate no. of elem

Vedclass · Accepted Answer

$8$

Vedclass · Answer

Here, $p , p ^{ n } \in\{1,2, \ldots 50\}$

Now p can take values

$2,3,5,7,11,13,17,23,29,31,37,41,43$ and $47 .$

we can calculate no. of elements in $R$, as

$\left(2,2^{\circ}ight),\left(2,2^{1}ight) \ldots\left(2,2^{5}ight)$

$\left(3,3^{\circ}ight), \ldots\left(3,3^{3}ight)$

$\left(5,5^{\circ}ight), \ldots\left(5,5^{2}ight)$

$\left(7,7^{\circ}ight), \ldots\left(7,7^{2}ight)$

$\left(11,11^{\circ}ight), \ldots\left(11,11^{1}ight)$

And rest for all other two elements each

$n \left( R _{1}ight)=6+4+3+3+(2 	imes 10)=36$

Similarly for $R _{2}$

$\left(2,2^{\circ}ight),\left(2,2^{1}ight)$

$\left(47,47^{\circ}ight),\left(47,47^{1}ight)$

$n \left( R _{2}ight)=2 	imes 14=28$

$n \left( R _{1}ight)- n \left( R _{2}ight)=36-28=8$

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