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Let \mathrm{R_{1} \, and\, R_{2}}  be relations on the set \mathrm{\{1,2, \ldots ., 50\}} such that
\mathrm{R_{1}=\left\{\left(p, p^{n}\right): p\right.} is a prime and \mathrm{n \geq 0} is an integer \mathrm{n \geq 0\}} and
\mathrm{R_{2}=\left\{\left(p, p^{n}\right): p\right. is\: a\: prime \; and \: n=0 \: or \: 1\}}.
Then, the number of elements in \mathrm{R_{1}-R_{2}} is _________.

Option: 1

8


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

\mathrm{R_{1}-R_{2}= \left \{ \left ( p,p^{n} \right ) :p\; \text{is a prime and } n\geq 2\, is\: an\; integer\right \}}
                   \mathrm{= \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 \}}.

No.of elements in \mathrm{R_{1}-R_{2}= 8}

Posted by

Ramraj Saini

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