JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R_{1}\) and \(R_{2}\) be relations on the set \(\{1,2, \ldots, 50\}\) such that \(R _{1}=\left\{\left( p , p ^{ n }\right)\right.\) : \(p\) is a prime and \(n \geq 0\) is an integer \(\}\) and \(R _{2}=\left\{\left( p , p ^{ n }\right)\right.\) : \(p\) is a prime and \(n =0\) or \(1\}\). Then, the number of elements in \(R _{1}- R _{2}\) is........
- A \(90\)
- B \(3\)
- C \(9\)
- D \(8\)
Answer & Solution
Correct Answer
(D) \(8\)
Step-by-step Solution
Detailed explanation
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 \(\left(2,2^{\circ}\right),\left(2,2^{1}\right) \ldots\left(2,2^{5}\right)\)…
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