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JEE Main 2024 · Mathematics · Sets, Relations and Functions · easy

How many reflexive relations can be defined on the set \p,q,r\?

Single correct option

How many reflexive relations can be defined on the set {p,q,r}\{p,q,r\}?
  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. Reflexivity forces the 33 pairs (a,a)(a,a) to be present, leaving the other 9−3=69-3=6 pairs free (each in or out). Hence the number is 26=642^6=64. The common error is to count all relations (29=5122^9=512).
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