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JEE Main 2018 · Mathematics · Sets, Relations and Functions · medium

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

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The number of reflexive relations on a set containing 4 elements is
  1. A. 2162^{16}
  2. B. 2122^{12}
  3. C. 262^{6}
  4. D. 242^{4}
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Answer: (B) 2122^{12}

A relation on a 4-element set is a subset of the 1616 ordered pairs. Reflexivity forces the 44 pairs (a,a)(a,a) to be present, so each of the other 16−4=1216-4=12 pairs may be included or not. Count =212=4096=2^{12}=4096.
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Original question written in the JEE Main 2018 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake