Relations
Counting Relations
Premium Question
Grade 11

Question:

The number of reflexive relations on a set with $n$ elements is:
(1) $2^{n^2}$
(2) $2^{n^2-n}$
(3) $2^n$
(4) $n!$

Step-by-Step Solution

Key Concept: A reflexive relation must include all $n$ diagonal pairs $(a, a)$ — these are fixed. The remaining $n^2 - n$ off-diagonal ordered pairs can each independently be included or excluded: $2^{n^2-n}$ choices.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)

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