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What is the possible number of reflexive relations on a set of 5 elements?

1. 2¹⁰
2. 2¹⁵
3. 2²⁰
4. 2²⁵

Correct answer: 2²⁰

Solution

A reflexive relation must contain all 5 diagonal pairs, fixing them. The remaining n^2 - n = 25 - 5 = 20 ordered pairs may each be present or absent freely, giving 2^20 reflexive relations (index 2), not 2^10.

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