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NDA 2018 Maths · Mathematics · Sets, Relations and Functions · medium

How many reflexive relations can be defined on a set A having 4 elements?

Single correct option

How many reflexive relations can be defined on a set AA having 4 elements?
  1. A. 2162^{16}
  2. B. 242^{4}
  3. C. 2122^{12}
  4. D. 444^{4}
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Answer: (C) 2122^{12}

A relation on AA is a subset of A×AA\times A (16 ordered pairs). Reflexivity forces the 4 diagonal pairs (a,a)(a,a) to be present; each of the remaining 16−4=1216-4=12 pairs is free to be in or out, giving 212=40962^{12}=4096. The trap is 2162^{16}, which counts all relations.
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Original question written in the NDA 2018 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