WBJEE · Maths · Sets and Relations
The number of reflexive relations on a set \(A\) of \(n\) elements is equal to
- A \(2^{n^2}\)
- B \(\mathrm{n}^2\)
- C \(2^{n(n-1)}\)
- D \(n^2-n\)
Answer & Solution
Correct Answer
(C) \(2^{n(n-1)}\)
Step-by-step Solution
Detailed explanation
Total number of ordered pair \(=\mathrm{n}^2\) Number of pair that can be included or excluded \(=n^2-n\) Each of the remaining \(\mathrm{n}^2-\mathrm{n}\) pairs we have two choices Include it in the relation or not include it So total no. of reflexive relation is \(2^{n(n-1)}\)
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