Let R _ 1 and R _ 2 be relations on the set \ 1, 2, , 50\ such that...

Here,& $p, p^{n} \in \left\{1, 2, \ldots 50\right\}$

Now~$p$~can take values

$2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43$~and& $47$.

$∴$~${R}_{1}= { \left(2, {2}^{0}\right), \left(2, {2}^{1}\right) \ldots \left(2, {2}^{5}\right),\left(3, {3}^{0}\right), \ldots \left(3, {3}^{3}\right),\left(5, {5}^{0}\right), \ldots \left(5, {5}^{2}\right),\left(7, {7}^{0}\right), \ldots \left(7, {7}^{2}\right),\left(11, {11}^{0}\right), \left(11, {11}^{1}\right), . . . \left(47, {47}^{0}\right), \left(47, {47}^{1}\right) }$

${R}_{2} = \left\{\left(2, {2}^{0}\right), \left(2, {2}^{1}\right), \left(3, {3}^{0}\right), \left(3, {3}^{1}\right) . . . . \left(47, {47}^{0}\right), \left(47, {47}^{1}\right)\right\}$

Now~${R}_{1} - {R}_{2} ≡ {R}_{1} \cap {R2}^{'}$

So~${R}_{1} - {R}_{2} = \left\{\left(2, {2}^{2}\right), \left(2, {2}^{3}\right), \left(2, {2}^{4}\right), \left(2, {2}^{5}\right), \left(3, {3}^{2}\right), \left(3, {3}^{3}\right), \left(5, {5}^{2}\right), \left(7, {7}^{2}\right)\right\}$

$∴ n\left({R}_{1} - {R}_{2}\right) = 8$