Project ForgeDiscrete Mathematics
Set Theory & Abstract Algebra
GATE 2010
Easy
What is the possible number of reflexive relations on a set of 5 elements?
- A2¹⁰
- B2¹⁵
- 2²⁰
- D2²⁵
Explanation
A relation on a 5-element set is a subset of the 5×5=25 possible ordered pairs. Reflexivity forces all 5 diagonal pairs (a,a) to be present (fixed), leaving 25-5=20 pairs free to be included or not — giving 2²⁰ reflexive relations.
Source: GATE CS 2010 (2010)
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