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JEE Main 2016 · Mathematics · Sets, Relations and Functions · easy

On a set having exactly 3 elements, how many reflexive relations can be defined?

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On a set having exactly 3 elements, how many reflexive relations can be defined?
  1. A. 6464
  2. B. 512512
  3. C. 88
  4. D. 6363
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Answer: (A) 6464

A relation on a 3-element set is a subset of the 99 ordered pairs. A reflexive relation must contain the 33 pairs (a,a)(a,a), while the remaining 9−3=69-3=6 pairs are free. Hence the count is 26=642^6=64. (512=29512=2^9 counts all relations.)
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