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NDA 2022 Maths · Mathematics · Sets, Relations and Functions · hard

The number of reflexive relations on a set with 4 elements is

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The number of reflexive relations on a set with 44 elements is
  1. A. 2122^{12}
  2. B. 2162^{16}
  3. C. 242^{4}
  4. D. 282^{8}
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Answer: (A) 2122^{12}

A relation on a 44-element set is a subset of the 1616 ordered pairs. Reflexivity forces the 44 pairs (a,a)(a,a) to be present, leaving 16−4=1216-4=12 free pairs, so there are 2122^{12} reflexive relations. 2162^{16} counts all relations.
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Original question written in the NDA 2022 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake